# Solve the System of Equations y=3x^2-7x+1 y=-4x+19

Solve the System of Equations y=3x^2-7x+1 y=-4x+19
Eliminate the equal sides of each equation and combine.
Solve for .
Move all terms containing to the left side of the equation.
Add to both sides of the equation.
Subtract from both sides of the equation.
Subtract from .
Factor the left side of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor.
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
Add to both sides of the equation.
Set equal to and solve for .
Set equal to .
Subtract from both sides of the equation.
The final solution is all the values that make true.
Evaluate when .
Substitute for .
Substitute for in and solve for .
Remove parentheses.
Simplify .
Multiply by .