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Mathematics
OpenStudy (anonymous):

solve 3x-4y=-4 over x+2y=-8

8 years ago
OpenStudy (anonymous):

I don't understand what's being asked.

8 years ago
OpenStudy (anonymous):

3x-4y=-4 x+2y=-8

8 years ago
OpenStudy (anonymous):

there's not enough information being shown

8 years ago
OpenStudy (shadowfiend):

That is enough information. I assume you're trying to solve for x and y.

8 years ago
OpenStudy (anonymous):

i agree ^^

8 years ago
OpenStudy (shadowfiend):

So the first step in these situations is ideally to try to get one of the variables in terms of the other. In this case, we'll try to get \(x\) in terms of \(y\). We'll pick the second equation because it's slightly easier: \[\begin{align} x + 2y &= -8\\ x &= -8 - 2y \end{align}\] So far, so good. We can now plug in for \(x\) in the first equation: \[3(-8 - 2y) - 4y = -4\] Now we can solve for \(y\): \[\begin{align} -24 - 6y - 4y &= -4\\ -24 - 10y &= -4\\ -10y &= -4 + 24 = 20\\ y &= \frac{20}{-10} = -2 \end{align}\] So we now know that \(y = -2\). We can plug \(y\) back into our equation for \(x\) and get \(x\): \[x = -8 - 2y = -8 - 2(-2) = -8 + 4 = -4\] Now we have that \(y = -2\) and \(x = -4\), but, we should plug back into both of the original equations to make sure that our result matches the equations: \[3x - 4y = 3(-4) - 4(-2) = -12 + 8 = -4\] That one matches. \[x + 2y = -4 + 2(-2) = -4 - 4 = -8\] And so does that one. The solution is right! Hope that helps.

8 years ago
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