8) $$ -7 x-2 y=-13 $$ $$ x-2 y=11 $$

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UpStudy AI · Accepted Answer

Solve the system of equations $$ -7x-2y=-13;x-2y=11 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}-7x-2y=-13\x-2y=11\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}-7x-2y=-13\x=11+2y\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$-7\left(11+2yight)-2y=-13$$
- step3: Simplify:
  $$-77-16y=-13$$
- step4: Move the constant to the right side:
  $$-16y=-13+77$$
- step5: Add the numbers:
  $$-16y=64$$
- step6: Change the signs:
  $$16y=-64$$
- step7: Divide both sides:
  $$\frac{16y}{16}=\frac{-64}{16}$$
- step8: Divide the numbers:
  $$y=-4$$
- step9: Substitute the value of $$y:$$
  $$x=11+2\left(-4ight)$$
- step10: Simplify:
  $$x=3$$
- step11: Calculate:
  $$\left\{ \begin{array}{l}x=3\y=-4\end{array}ight.$$
- step12: Check the solution:
  $$\left\{ \begin{array}{l}x=3\y=-4\end{array}ight.$$
- step13: Rewrite:
  $$\left(x,yight) = \left(3,-4ight)$$
The solution to the system of equations is $$ (x,y) = (3,-4) $$.
$$ x=3 $$ and $$ y=-4 $$.

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