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-4x-6y=-8 x=3y-34

Solve the system of equations
Answer has to be an ordered paired help

User Cyphar
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1 Answer

5 votes

Answer:

Answer as an ordered pair in (x, y) form: (-10, 8)

Explanation:

Method to solve: Substitution:

The system of equations is already arranged in such a way that allows us to first solve for y by substituting x = 3y - 34 for x in -4x - 6y = -8:

Solving for y by substituting x = 3y - 34 for x in -4x - 6y = -8:

-4(3y - 34) - 6y = -8

(-12y - 6y) + 136 = -8

(-18y + 136 = -8) - 136

(-18y = -144) / -18

y = 8

Thus, y = 8

Solving for x:

We can solve for x by plugging in 8 for y in any of the two equations in the system.

Let's use x = 3y - 34:

x = 3(8) - 34

x = 24 - 34

x = -10

Thus, x = -10.

Therefore, the answer (i.e., the solution to the system) as an ordered pair in (x, y) form is (-10, 8).

Optional Step: Checking the validity of our answer:

We can check that our answer is correct by plugging in -10 for x and 8 for y in both equations in the system and seeing if we get the same answer on both sides of the equation when simplifying:

Checking x = -10 and y = 8 in -4x - 6y = -8:

-4(-10) - 6(8) = -8

40 - 48 = -8

-8 = -8

Checking x = -10 and y = 8 in x = 3y - 34:

-10 = 3(8) - 34

-10 = 24 - 34

-10 = -10

Thus, our answer is correct.

User Impl
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