Question

What is the value of the y variable in the solution to the following system of equations?
13x - 6y = 20
7x + 4y = 18

2

1

-2

-1

Answer 1

13x - 6y = 20
7x + 4y = 18

Since we want to know solve for y, we need to get the x terms to cancel out.
Notice that the x term in the first equation has a coefficient of 13, and the x term in the second equation has a coefficient of 7.
If we multiply each equation by the opposite coefficient, we can get the x terms to cancel out.
So multiply the first equation by 7 and the second equation by 13.
(7)(13x - 6y) = (7)(20)
(13)(7x + 4y) = (13)(18)

91x - 42y = 140
91x + 52y = 234

Notice how the x terms have the same coefficients now?
To get them to cancel, subtract bottom equation from top equation.
Let us do this one term at a time.
We start with the first terms.
91x - 91x = 0
Next do the second terms
-42y - 52y = -94y
Finally, do the numbers on the right side of the equal sign.
140 - 234 = -94

Now combine all three terms.
0 - 94y = -94
-94y = -94
divide both sides by (-94)
-94y/(-94) = -94/(-94)
y = 1