Answer:
y = -2 and x = 4
Explanation:
8x + 14y = 4
-6x - 7y = -10
First, find the lowest common multiple of 8 and 6 (which is 24). Multiply the first equation by 3:
8x + 14y = 4
3(8x + 14y) = 3(4)
24x + 42y = 12
Multiply the second equation by 4:
-6x - 7y = -10
4(-6x - 7y) = 4(-10)
-24x - 28y = -40
Now, add the two equations together:
24x + 42y = 12
-24x - 28y = -40
24x + -24x = 0
42y + -28y = 14y
12 + -40 = -28
14y = -28
Divide both sides by 14:
14y ÷ 14 = -28 ÷ 14
y = -2
Plug this known variable back into the first equation:
8x + 14(-2) = 4
8x + (-28) = 4
8x - 28 = 4
Add 28 to both sides:
8x - 28 + 28 = 4 + 28
8x = 32
Divide both sides by 8:
8x ÷ 8 = 32 ÷ 8
x = 4
So y = -2 and x = 4.
Hope this helps!