How do you solve the following system?: 13x +17y =11, -6x +5y = -2713x+17y=11,6x+5y=27

1 Answer
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 = -276x+5y=27
-6x = -5y - 276x=5y27
x = 5/6y + 4.5x=56y+4.5

Then, insert the last expression in the other equation:
13x+17y=1113x+17y=11
13(5/6y+4.5)+17y=1113(56y+4.5)+17y=11
65/6y+58.5+17y=11656y+58.5+17y=11
65/6y+102/6y=-58.5+11656y+1026y=58.5+11
167/6y = -47.51676y=47.5
167/6y = -285/61676y=2856
167y = -285167y=285
y = -285/167y=285167 which is around -1.7066.

Then, replace the found y in the equation with isolated x to find x:
x=5/6*(-285/167) + 4.5x=56(285167)+4.5
x=3.0778x=3.0778

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