Solve the system of equations by substitution:

\[
-5x - 8y = 17
\]

\[
2x - 7y = -17
\]

\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

Answered by Anonymous | 2024-06-10

− 5 x = 17 + 8 y x = − 5 17 + 8 y ​ 2 x − 7 y = − 17 2 ∗ 5 17 + 8 y ​ − 7 y = − 17 5 34 + 16 y ​ − 7 y = − 17 w e b r in g t o t h e s am e d e n o mina t or 34 + 16 y − 35 y = − 85 − 19 y = − 85 − 34 19 y = 119 y = 19 119 ​ x = − 5 17 + 8 ∗ 19 119 ​ ​ x = − 5 17 + 19 952 ​ ​ x = − 5 19 323 + 952 ​ ​ x = − 5 19 1275 ​ ​ x = − 19 1275 ​ ∗ 5 1 ​ x = − 19 255 ​

Answered by mariamikayla | 2024-06-10

The solution to the system of equations is (x, y) = (-5, 1). This was found by solving one equation for x and substituting it into the other equation. After solving, we determined that y = 1 and subsequently that x = -5.
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Answered by Anonymous | 2024-12-24