Question

When you are given one quadratic equation and one linear equation what do you do to solve it algebraically to find the solutions rather than graphing it. Example in the picture

Answer 1

`y=2x^2-4x+3`

`y=4x-5`

both equation having y on the left side

So we can equate the right side of the equation

`2x^2-4x+3 = 4x-5`

Subtract 4x on both sides

`2x^2-8x+3 = -5`

Add 5 on both sides

`2x^2-8x+8 = 0`

Now we solve for x

Divide the whole equation by 2

`x^2-4x+4 = 0`

(x-2)(x-2)=0

(x-2)^2 =0

So x= 2

Now we find out y when x=2

y=4x-5

y= 4(2) -5

y = 8 -5 = 3

So solution is x=2 and y = 3

(2,3)