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

1 Answer
Alan P.
Apr 10, 2018

(x,y)=( -11 16/53,-6 3/53)(x,y)=(−111653,−6353)

Explanation:

Given
[1]color(white)("XXX")5x-9y=-2XXX5x−9y=−2
[2]color(white)("XXX")7x-2y=-67XXX7x−2y=−67

Convert to equivalent equations with the same coefficient for yy
by multiplying [1] by 22
and multiplying [2] by 99
[3]color(white)("XXX")10x-18y=-4XXX10x−18y=−4
[4]color(white)("XXX")63x-18y=-603XXX63x−18y=−603

Subtract [3] from [4] to eliminate the yy term
[5]color(white)("XXX")53x=-599XXX53x=−599

Divide both sides of [5] by 5353
[6]color(white)("XXX")x=-599/53= -11 16/53XXXx=−59953=−111653

We could substitute -599/53−59953 for xx in one of the given equation (either one) and solve for yy
or repeat a similar process to the one above to eliminate the xx factors:

Multiply [1] by 77 and [2] by 55
[7]color(white)("XXX")35x-63y=-14XXX35x−63y=−14
[8]color(white)("XXX")35x-10y=-335XXX35x−10y=−335

Subtract [7] from [8]
[9]color(white)("XXX")53y=-321XXX53y=−321

Divide both sides of [9} by 5353
[10]color(white)("XXX")y=-321/53=-6 3/53XXXy=−32153=−6353

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