Question

Solve the system by the method of substitution.
2x^2 + 4x − y = 19
2x − y = −5

Answer 1

Hang on a sec

Answer 2

okay

Answer 3

The goal here is to get one of the equations all in terms of one variable. If you managed to get the first equation in terms of x only, it would simplify to a quadratic equation. From there you using factoring methods.

Answer 4

im suppose too find two (x,y) but I got it wrong.

Answer 5

Re-writing the second equation,
y = 2x + 5

You can substitute the expression for y into the first equation to get:

2x^2 + 4x - (2x + 5) = 19

Answer 6

We will find the (x,y) pair I assure you. But first, we needed to replace y with an appropriate expression for x that would work.

Answer 7

i got 2x^2+2x-24=0

Answer 8

then factor for x?

Answer 9

Well, if you factor out 2 on the left side first, you'll get
2(x^2 - x - 12) = 0

Then divide both sides by 2 to get
x^2 - x - 12 = 0

That should make it easier to factor.

Answer 10

x=-3 and4?

Answer 11

x^2 - x - 12 = 0
x^2 -4x + 3x -4*3 = 0
x(x - 4) + 3(x - 4) = 0
(x - 4)(x + 3) = 0

Answer 12

so now i plug in 4 and -3 to find y?

Answer 13

i got (4,13) and (-3,-1) and it was wrong

Answer 14

I made a sign mistake

x^2 + x - 12 = 0

Factor that

Answer 15

\[(x-3) (x+4)=0 \]