Solve using elimination.
5x + 4y = 8
-5x 3y = -1
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5x + 4y = 8

-5x + 3y = -1

Let's add both equations, to eliminate x.

5x + 4y - 5x + 3y = 8 - 1

7y = 7

y = 1

Let us substitute this value of y in equation 1, so we can find x.

5x + 4 = 8

5x = 4

x = 4/5

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4