Solve the following system of equations:5𝑥−6𝑦=−81.54𝑥+2𝑦=−4 𝑥 = 𝑦 =
Question
Solve the following system of equations:5𝑥−6𝑦=−81.54𝑥+2𝑦=−4 𝑥 = 𝑦 =
Solution
To solve the system of equations:
5x - 6y = -81.5 4x + 2y = -4
We can use the method of substitution or elimination. Here, I'll use the elimination method.
First, let's make the coefficients of y the same in both equations. We can do this by multiplying the second equation by 3:
12x + 6y = -12
Now we have:
5x - 6y = -81.5 12x + 6y = -12
We can add these two equations together:
5x + 12x = -81.5 - 12 17x = -93.5
Now, solve for x:
x = -93.5 / 17 x = -5.5
Substitute x = -5.5 into the first equation:
5(-5.5) - 6y = -81.5 -27.5 - 6y = -81.5 -6y = -81.5 + 27.5 -6y = -54 y = -54 / -6 y = 9
So, the solution to the system of equations is x = -5.5 and y = 9.
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