Solving with Elimination Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
4 of 54 of 5 Items

Question
Solve the system of equations.
–x+6y=13
4x–10y=–10(1 point)
(
,
)

Answer 1

To solve this system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations together. Let's start by multiplying the first equation by 4 and the second equation by -1:

-4x + 24y = 52
-4x + 10y = 10

Now, let's add these two equations together:

-4x + 24y + -4x + 10y = 52 + 10
34y = 62
y = 62/34
y = 31/17

Now that we have found the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

-x + 6(31/17) = 13
-x + 186/17 = 13
-x = 13 - 186/17
-x = (221 - 186)/17
-x = 35/17
x = -35/17

Therefore, the solution to the system of equations is:
(x, y) = (-35/17, 31/17)