To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.
First, we will multiply both sides of the second equation by 4 to eliminate the x-term. This gives us:
28x - 12y = 196
Now, we can subtract the first equation from this equation to eliminate the x-term:
(28x - 12y) - (4x + 7y) = 196 - (-33)
28x - 12y - 4x - 7y = 196 + 33
24x - 19y = 229
Now we have a new equation:
24x - 19y = 229
We can solve this new equation for x:
24x = 229 + 19y
x = (229 + 19y) / 24
Now we can substitute this expression for x into one of the original equations (either one will work). Let's use the first equation:
4x + 7y = -33
4((229 + 19y) / 24) + 7y = -33
(229 + 19y) / 6 + 7y = -33
To simplify this equation, we can multiply every term by 6 to eliminate the fraction:
229 + 19y + 42y = -198
61y = -427
y = -7
Now we can substitute this value for y back into the equation we found for x:
x = (229 + 19(-7)) / 24
x = (229 - 133) / 24
x = 96 / 24
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -7.
4x + 7y = -33
7x - 3y = 49
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