How do you solve the following linear system: x + 2y = 13, 3x + 2y = 5 ?

1 Answer
Mar 15, 2018

x=-4

y=8.5

Explanation:

First, line up the equations as an addition problem:

___x + 2y=13
+ 3x+2y=5

As you can see, both equations have a 2y in common, so this is what you need to eliminate in order to find the value of x. To do this, multiply the entire second equation by -1:

(-1) x (3x+2y=5) -> -3x-2y=-5

Now, put the addition problem back together:

..........x + 2y=13
+ -3x-2y=-5
________,
..........-2x=8

Now, divide each side by -2 to isolate x:

(-2x)/-2=8/-2 -> x=-4

Since we know the value of x is -4 now, we can substitute -4 in for x in either equation. Let's use the first one:

(-4) + 2y=13

Add 4 to both sides of the equation to isolate 2y:

(-4)+ 2y=13
+4 ......................+4
______,
...................2y=17

Now, divide each side by 2 to isolate y:

(2y)/2=17/2 -> y=8.5