Answer:
x = -4; y = 12
Explanation:
Step 1: Multiply the first equation by 4 and the second equation by -7:
4(7x - 2y = -52)
-7(4x + 7y = 68)
---------------------------------------------------------------------------------------------------------- 28x - 8y = -208
-28x - 49y = -476
Step 2: Add the two equations to cancel the xs:
(28x + (-28x)) + (-8y + (-49y)) = (-208 + (-476))
-57y = -684
Step 3: Divide both sides by -57 to find y:
y = 12
Step 4: Plug in 12 for y in the first equation to find x:
7x - 2(12) = -52
7x - 24 = -52
Step 5: Add 24 to both sides:
(7x - 24 = -52) + 24
7x = -28
Step 6: Divide both sides by 7 to find x:
(7x = -28) / 7
x = -4
Thus, y = 12 and x = -4
Optional Step 7: Check the validity of our answers:
We can check that our answers are correct by plugging in 12 for y and -4 for x in both equations in our system and see whether we get -52 for the first equation and 68 for the second equation:
Checking answers for the first equation:
7(-4) - 2(12) = -52
-28 - 24 = -52
-52 = -52
Checking answers for the second equation:
4(-4) + 7(12) = 68
-16 + 84 = 68
68 = 68
Thus, our answers are correct.