Question

Solving Systems of Equations by substitution
-5x-8y=17
2x-7y=-17

Answer 1

`-5x=17+8y \\ x= - (17+8y)/(5) \\ 2x-7y=-17 \\ 2* (17+8y)/(5) -7y=-17 \\ (34+16y)/(5) -7y=-17 \ we \ bring \ to \ the \ same \ denominator \ \\34+16y-35y=-85 \\ -19y=-85-34 \\ 19y=119 \\ y= (119)/(19) \\ x= -( 17+ 8* (119)/(19) )/(5) \\ x= - ( 17 + (952)/(19) )/(5) \\ x= - ( (323+952)/(19))/(5) \\ x= -( (1275)/(19) )/(5) \\ x= -(1275)/(19) * (1)/(5) \\ x= -(255)/(19)`

Answer 2

`\left\{\begin{array}{ccc}-5x-8y=17\\2x-7y=-17\end{array}\right\\\left\{\begin{array}{ccc}-5x=8y+17&/\cdot(-2)\\2x-7y=-17&/\cdot5\end{array}\right\\\\\left\{\begin{array}{ccc}10x=-16y-34\\10x-35y=-85\end{array}\right\\\\substitute:\\\\-16y-34-35y=-85\\-51y=-85+34\\-51y=-51\ \ \ \ /:(-51)\\y=1\\\\10x=-16\cdot1-34\\10x=-50\ \ \ \ /:10\\x=-5\\\\Solution:x=-5\ and\ y=1`