What is the solution set to the following system of equations?

Question

Y=2x-3

Y=-x^2+5x+1

Answer 1

y = 2x - 3
y = -x² + 5x + 1

 

2x - 3 = -x² + 5x + 1

 

Algebra 2? You should be able to solve for x and answer.

Answer 2

Substitute 2x-3 into the value for y in the second equation.

So now we have: 2x-3 = -x^2+5x+1

One side has to be equal to 0 in order to factor, so now we are left with:

-x^2+3x+4 = 0

Once factored, we are left with: (-x+4)(x+1) = 0

 

So, the solution set is:

x = 4 and x = -1.

Plugging these x-values back into the equation for y...

y = 5 and y= -5.