How do you solve by substitution x+-y=1 and -2x+y=4?

1 Answer
Sep 8, 2015

The problem has two solutions:
x=-1,y=2.
x=-5,y=-6.

Explanation:

To solve by substitution, we isolate one of the variables in one equation, and use that to solve the other equation.

x+-y =1 shows two cases: x+y=1 or x-y=1.

Case 1:
Our system is:

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

Since the first equation is easier to work with, we can isolate a variable there.
x+y=1
x=1-y

Now, we substitute 1-y into x in the other equation, and simplify.

-2x+y=4
-2(1-y)+y=4
-2+2y+y=4
3y=6
y=2

We now know the value of y, which we can use to solve for x using either equation:

x+y=1
x+2=1
x=-1

Therefore, the solution to Case 1 is x=-1,y=2.

Case 2:
Our system is:

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

Like before, we isolate one of the variables in one equation and solve using the other equation.

x-y=1
x=1+y

-2x+y=4
-2(1+y)+y=4
-2-2y+y=4
-y=6
y=-6

At this point, we know the y=-6, so we can solve for x using either equation:

x-y=1
x+6=1
x=-5

Therefore the solution to case 2 is x=-5,y=-6.

The problem has two solutions:
x=-1,y=2.
x=-5,y=-6.