Question

Solve the system of equations.y= 2x + 4y = x2 + x - 2​

Answer 1

Answer:

A.

Step-by-step explanation:

$y=2x+4$

$y=x^2+x-2$

Both equations are solved for y so I'm just going to substitute

the 1st  y  (the 2x+4) into the second equation's y.

$2x+4=x^2+x-2$

I'm going to get everything on one side so I have 0=ax^2+bx+c.

Subtract 2x and subtract 4 on both sides:

$0=x^2-x-6$

Since the coefficient of x^2 is 1, all we have to do is find two numbers that multiply to be -6 and add up to be -1.

These numbers are -3 and 2.

So the factored form of our equation is:

$0=(x-3)(x+2)$

This means we have x-3=0 or x+2=0.

x-3=0

Add 3 on both sides:

x=3

x+2=0

Subtract 2 on both sides:

x=-2

So now we need to find y. I'm going to choose to use the easier equation:

y=2x+4.

If x=3, then y=2(3)+4=6+4=10.  The ordered pair (3,10) is a solution.

If x=-2, then y=2(-2)+4=-4+4=0.  The orded pair (-2,0) is a solution.