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 = 5/6y + 4.5#

Then, insert the last expression in the other equation:
#13x+17y=11#
#13(5/6y+4.5)+17y=11#
#65/6y+58.5+17y=11#
#65/6y+102/6y=-58.5+11#
#167/6y = -47.5#
#167/6y = -285/6#
#167y = -285#
#y = -285/167# which is around -1.7066.

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

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

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