To solve the system of equations by elimination, we will follow the steps below:
-3x+8y=73 ----------------------------(1)
x-7y=-46 -------------------------------(2)
First we will eliminate x
To eliminate x, we have to make the coefficients to be the same. This can be achieved by muliplying through equation(1) by 1 and equation (2) by 3
The results of the multiplication is;
-3x + 8y = 73 -------------------------(3)
3x - 21y =-138 ---------------------------------(4)
Then, we can now eliminate x by adding equation (3) and equation(4)
The result of the addition is;
-13y = -65
divide both-side of the equation by -13
y = 5
Next, we move on to eliminate y and solve for x
we make sure that the coefficients of y in the 2 equations are the same. This can be achieved by multiplying equation(1) by 7 and equation(2) by 8
The result of the multiplication is;
-21x + 56y = 511 -----------------------------(5)
8x - 56y = -368 ----------------------------------(6)
add equation (5) and equation(6)
-13x = 143
divide both-side of the equation by -13
x= -11