Question

Y= - x+2 Y=3x-4
Estimate the solution to the system of equations

Answer 1

`x=(3)/(2)\\ y=(1)/(2)`

Explanation:

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

Let's solve one of them for x.

`y=3x-4`

Add 4

`y+4=3x`

Divide by 3.

`x=(y+4)/(3)`

Now, plug the value of y in the formula, or you can plug the value of x in the other equation. I'll take this one.

`x=(y+4)/(3)`

`x=((-x+2)+4)/(3)`

`x=(-x+2+4)/(3)`

`x=(-x+6)/(3)`

Multiply by 3 to get rid of the denominator.

`3x=-x+6`

add x

`3x+x=6`

Combine like terms;

`4x=6`

Divide by 4.

`x=(6)/(4)`

Simplify.

`x=(3)/(2)`

Now that you found the value of x, replace it in any of the equations to find y.

`y=-x+2\\y=-((3)/(2))+2\\ y=-(3)/(2)+2`

`y=(-3+2*2)/(2) \\y=(-3+4)/(2) \\y=(1)/(2)`

Proof:

`y=3x-4\\(1)/(2)=3((3)/(2))-4\\(1)/(2)=((9)/(2))-4`

`(1)/(2)=(9-4*2)/(2)`

`(1)/(2)=(9-8)/(2)`

`(1)/(2)=(1)/(2)`