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.