How do you solve the system of equations 13x+9y=155 and 14x+10y=166?

1 Answer
Andy Y.
Jun 21, 2017

(986,−1407)

Explanation:

The first step is to solve one of the equations (it doesn't matter which one) for y in terms of x.

14x+10y=166

Subtract 10y from both sides

14x=−10y+166

Divide both sides by 14

x=−1014y−16614

Reduce the fractions to lowest terms

x=−57y−1337

Next, take the expression equal to x and plug it into the other equation.

13x+9y=155

13(−57y−1337)+9y=155

−657y−17297+9y=155

Multiply everything by 7 to get rid of all fractions

−65y−1729+63y=1085

Combine like terms

−2y=2814

Divide both sides by −2

y=−1407

Finally, plug this value for y back into the equation for x

x=−57y−1337

x=−57(−1407)−19

x=−5(−201)−19

x=1005−19

x=986

So the solution to both equations is (986,−1407)

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