How do you solve the following system?: 13x+17y=11,−6x+5y=−27

1 Answer
Constantin B.
Dec 10, 2017

Express y in terms of x and insert the expression in the other equation.

Explanation:

Substitution means expressing one variable in terms of another. So, you'll need to remake the expression in such a way that x (or y, doesn't matter) will be alone on one side of the equation.

Let's pick the second one for this, since it seems easier:
−6x+5y=−27
−6x=−5y−27
x=56y+4.5

Then, insert the last expression in the other equation:
13x+17y=11
13(56y+4.5)+17y=11
656y+58.5+17y=11
656y+1026y=−58.5+11
1676y=−47.5
1676y=−2856
167y=−285
y=−285167 which is around -1.7066.

Then, replace the found y in the equation with isolated x to find x:
x=56⋅(−285167)+4.5
x=3.0778

And finally, the answer is:
x=3.0778
y=−1.7066

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