What is the solution for x plus y equals 1 and -4x plus 2y equals -2?

Answer 1

OK, there's two ways to solve systems of linear equations. The first way is substitution and the second way is called elimination/addition, but we're only going to solve it this way (because it's hard to show the other way just with text).

Let's do the simplest first, the substitution. You have:

x+y=1 and -4x+2y=-2

Solve for one of the variables (x or y) on the first equation. For example, solve for y in x+y=1:

x+y=1

y=1-x ;Subtract x on both sides

Now substitute 1-x into every y on the other equation:

-4x+2y=-2

-4x+2(1-x)=-2 ;Plug in 1-x into all the y's

-4x+2-2x=-2 ;Distribute the 2

-6x+2=-2 ;Combine the x's

-6x=-4 ;Subtract 2 to both sides

x=(-4/-6) ;Divide both sides by -6

x=2/3 ;Simplify the fraction

Now that you have what x is equal to, plug that back into y=1-x:

y=1-(2/3) ;Plug in 2/3 for x

y=1/3

Your solution for both equations is ( 2/3 , 1/3 ).