Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the equation.

Subtract <math><mstyle displaystyle="true"><mn>4</mn><mi>y</mi></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>3</mn><mi>z</mi></mstyle></math> from both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>5</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>4</mn><mi>y</mi><mo>-</mo><mn>3</mn><mi>z</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>5</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>4</mn><mi>y</mi><mo>-</mo><mn>3</mn><mi>z</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

Move the negative in front of the fraction.

Replace all occurrences of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn><mi>x</mi><mo>-</mo><mn>6</mn><mi>y</mi><mo>+</mo><mn>10</mn><mi>z</mi><mo>=</mo><mn>10</mn></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>4</mn><mi>y</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>3</mn><mi>z</mi></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> .

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>4</mn><mi>y</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>3</mn><mi>z</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>)</mo></mrow><mo>-</mo><mn>6</mn><mi>y</mi><mo>+</mo><mn>10</mn><mi>z</mi></mstyle></math> .

Simplify each term.

Apply the distributive property.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>4</mn><mi>y</mi></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> into the numerator.

Factor <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>3</mn><mi>z</mi></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> into the numerator.

Factor <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Simplify by adding terms.

Subtract <math><mstyle displaystyle="true"><mn>6</mn><mi>y</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn><mi>y</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>3</mn><mi>z</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>10</mn><mi>z</mi></mstyle></math> .

Replace all occurrences of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in <math><mstyle displaystyle="true"><mn>5</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>+</mo><mn>3</mn><mi>z</mi><mo>=</mo><mn>5</mn></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>4</mn><mi>y</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>3</mn><mi>z</mi></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> .

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><mn>5</mn><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>4</mn><mi>y</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>3</mn><mi>z</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>)</mo></mrow><mo>+</mo><mn>3</mn><mi>y</mi><mo>+</mo><mn>3</mn><mi>z</mi></mstyle></math> .

Simplify each term.

Apply the distributive property.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>4</mn><mi>y</mi></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> into the numerator.

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>3</mn><mi>z</mi></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> into the numerator.

Cancel the common factor.

Rewrite the expression.

Simplify by adding terms.

Combine the opposite terms in <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>y</mi><mo>-</mo><mn>3</mn><mi>z</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>+</mo><mn>3</mn><mi>z</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>z</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn><mi>z</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>3</mn><mi>y</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>y</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn><mi>y</mi></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mi>y</mi><mo>=</mo><mn>5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Simplify the left side.

Dividing two negative values results in a positive value.

Divide <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Replace all occurrences of <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> in <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>13</mn><mi>z</mi><mo>=</mo><mn>10</mn></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> .

Simplify the left side.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> .

Replace all occurrences of <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> in <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mn>4</mn><mi>y</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>3</mn><mi>z</mi></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> .

Simplify the right side.

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn><mrow><mo>(</mo><mo>-</mo><mn>5</mn><mo>)</mo></mrow></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>4</mn><mo>⋅</mo><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Move all terms not containing <math><mstyle displaystyle="true"><mi>z</mi></mstyle></math> to the right side of the equation.

Subtract <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>13</mn><mi>z</mi><mo>=</mo><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>13</mn><mi>z</mi><mo>=</mo><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>z</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Replace all occurrences of <math><mstyle displaystyle="true"><mi>z</mi></mstyle></math> in <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>4</mn><mo>-</mo><mfrac><mrow><mn>3</mn><mi>z</mi></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> with <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Simplify the right side.

Simplify <math><mstyle displaystyle="true"><mn>4</mn><mo>-</mo><mfrac><mrow><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> .

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>3</mn><mo>⋅</mo><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The solution to the system is the complete set of ordered pairs that are valid solutions.

The result can be shown in multiple forms.

Point Form:

Equation Form:

Do you know how to Solve the System of Equations 5x+4y+3z=0 -5x-6y+10z=10 5x+3y+3z=5? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.