Eliminate the equal sides of each equation and combine.

Move all terms containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the left side of the equation.

Add <math><mstyle displaystyle="true"><mn>4</mn><mi>x</mi></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>7</mn><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn><mi>x</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>19</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>19</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Factor the left side of the equation.

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>18</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>18</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>+</mo><mn>3</mn><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mn>3</mn><mrow><mo>(</mo><mo>-</mo><mn>6</mn><mo>)</mo></mrow></mstyle></math> .

Factor.

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mi>x</mi><mo>-</mo><mn>6</mn></mstyle></math> using the AC method.

Consider the form <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> . Find a pair of integers whose product is <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> . In this case, whose product is <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Write the factored form using these integers.

Remove unnecessary parentheses.

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>3</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>3</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to both sides of the equation.

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>+</mo><mn>2</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>+</mo><mn>2</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> from both sides of the equation.

The final solution is all the values that make <math><mstyle displaystyle="true"><mn>3</mn><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Substitute <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Substitute <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>⋅</mo><mn>3</mn><mo>+</mo><mn>19</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Remove parentheses.

Simplify <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mo>⋅</mo><mn>3</mn><mo>+</mo><mn>19</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>12</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>19</mn></mstyle></math> .

Substitute <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Substitute <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>⋅</mo><mo>-</mo><mn>2</mn><mo>+</mo><mn>19</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Remove parentheses.

Simplify <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mo>⋅</mo><mo>-</mo><mn>2</mn><mo>+</mo><mn>19</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>19</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 y=3x^2-7x+1 y=-4x+19? 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.

Name | three hundred seventy-two million sixty-six thousand sixty-one |
---|

- 372066061 has 8 divisors, whose sum is
**384290048** - The reverse of 372066061 is
**160660273** - Previous prime number is
**3361**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 31
- Digital Root 4

Name | one billion four hundred fifty-seven million eight hundred thirty-two thousand five hundred seventy-six |
---|

- 1457832576 has 1024 divisors, whose sum is
**33336178560** - The reverse of 1457832576 is
**6752387541** - Previous prime number is
**271**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 48
- Digital Root 3

Name | one billion four hundred seventy-eight million one hundred thirty-five thousand one hundred seventy-one |
---|

- 1478135171 has 4 divisors, whose sum is
**1498383672** - The reverse of 1478135171 is
**1715318741** - Previous prime number is
**73**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 38
- Digital Root 2