10 x= 17 y− 8
x= (17/10)y− 8/10
The second equation morphs as follows:
− 11 x+ 41 y= 7
− 11 x=− 41 y+ 7
11 x= 41 y− 7
x= (41/11)y− 7/11
Now we mix the right-hand sides, getting a first-degree equation in y:
(17/10)y− 8/10 = (41/11)y− 7/11Let’s get a common denominator here. We can multiply the numerators and denominators on the left side
of the equals sign by 11, and multiply the numerators and denominators on the right side of the equals
sign by 10. That gives us
(187/110)y− 88/110 = (410/110)y− 70/110Multiplying the whole equation through by 110 to get rid of the fractions, we obtain
187 y− 88 = 410 y− 70Adding 88 to each side produces
187 y= 410 y+ 18Subtracting 410y from each side, we have
− 223 y= 18We can divide through by −223 to get y= 18/(−223)=−18/223. This agrees with the result we obtained
by double elimination. We can plug this into either of the SI equations we derived above, solving for x.
The first equation will do. Step-by-step:
x= (17/10)y− 8/10
= (17/10)(−18/223)− 8/10
=−306/2,230− 8/10
=−306/2,230− 1,784/2,230
= (− 306 − 1,784)/2,230
=−2,090/2,230
=−209/223
Solve the Two-by-Two 287