To solve the system of equations using the process of elimination, we want to eliminate one variable by multiplying one or both equations by proper multiples so that the coefficients of one variable will cancel each other when added or subtracted.
In this case, we can eliminate x by multiplying the first equation by 3 and the second equation by -1. This will make the coefficients of x in both equations have the same absolute value (3) but opposite signs.
So, let's multiply the first equation by 3 and the second equation by -1:
3(-x + 6y) = 3(-9)
-3x + 18y = -27
-1(-3x + 8y) = -1(3)
3x - 8y = -3
Now, we can add these two equations to eliminate x:
(-3x + 18y) + (3x - 8y) = -27 + (-3)
10y = -30
Divide both sides of the equation by 10:
10y/10 = -30/10
y = -3
Now, substitute this value of y back into one of the original equations to solve for x.
Plugging y = -3 into the first equation:
-x + 6(-3) = -9
-x - 18 = -9
Add 18 to both sides:
-x = 9
Divide by (-1) to solve for x:
x = -9
Therefore, the solution to the given system of equations is x = -9 and y = -3.
-x + 6y = -9 and -3x + 8y = 3
use process of elimination
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