Carcass wrote:
If 3x + 2y = 24, and \(\frac{7y}{2x}= 7\), then y =
enter your value
Let's deal with 7y/2x = 7 first.
Multiply both sides by 2x to get: 7y = 14x
Divide both sides by 7 to get:
y = 2xASIDE: At this point, I COULD take 3x + 2y = 24 and replace y with 2x to get 3x + 2(2x) = 24 and solve the equation for x. HOWEVER, the question asks us to find the value of y. So, we'd need to then take that x-value and plug it in to one of the two equations and then solve THAT equation for y.
Rather than solve an extra equation, let's do the following:
We have:
y = 2xDivide both sides by 2 to get: y/2 = x
Now, we can take 3x + 2y = 24 and replace x with y/2 to get 3(y/2) + 2y = 24
[we now have an equation that we can directly solve for y!]Simplify: 3y/2 + 2y = 24
Multiply both sides by 2 to get: 3y + 4y = 48
Simplify: 7y = 48
Solve: y = 48/7
Answer: 48/7
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Brent Hanneson - founder of Greenlight Test Prep