How do you solve the following system: 5x−9y=−2,7x−2y=−67?

1 Answer
Alan P.
Apr 10, 2018

(x,y)=(−111653,−6353)

Explanation:

Given
[1]XXX5x−9y=−2
[2]XXX7x−2y=−67

Convert to equivalent equations with the same coefficient for y
by multiplying [1] by 2
and multiplying [2] by 9
[3]XXX10x−18y=−4
[4]XXX63x−18y=−603

Subtract [3] from [4] to eliminate the y term
[5]XXX53x=−599

Divide both sides of [5] by 53
[6]XXXx=−59953=−111653

We could substitute −59953 for x in one of the given equation (either one) and solve for y
or repeat a similar process to the one above to eliminate the x factors:

Multiply [1] by 7 and [2] by 5
[7]XXX35x−63y=−14
[8]XXX35x−10y=−335

Subtract [7] from [8]
[9]XXX53y=−321

Divide both sides of [9} by 53
[10]XXXy=−32153=−6353

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