Question

x/5 - y/10 = 4 and 3x/4 + 2y/3 = 8
Use substitution to find the solutions (if any).

Answer 1

x = 416/25 and y = -168/25

Answer 2

Okay. So what you are being asked to do is this. Solve one equation and then plug in the value of the variable into the other.
So starting with the first equation: (x/5 - y/10 = 4)
Multiply both sides by 5. Then you have;
x - y/2 = 4
Multiply both sides by 2:
2x - y = 4
-y = -2x + 4
y = 2x - 4
Now we can substitute for y in the second equation (3x/4 + 2y/3 = 8)
3x/4 + 2(2x-4)/3 = 8
3x/4 + (4x - 8)/3 = 8
Let's eliminate the denominators:
Multiply both sides by 4.
3x + 4(4x-8)/3 = 8
Multiply both sides by 3.
9x + 4(4x-8) = 8
Distribute:
9x + 16x - 32 = 8
Add like terms and add 32 to both sides.
25x = 24
x = 24/25
y = 2x - 4
There you go. If this helps, please leave a medal.
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