$$ \left. \begin{array} { l }{ ( 5 , - 8 ) ; 9 x + 7 y = - 11 } \ { - 2 x - 5 y = 30 } \end{array} ight. $$

Question

$$ \left. \begin{array} { l }{ ( 5 , - 8 ) ; 9 x + 7 y = - 11 } \ { - 2 x - 5 y = 30 } \end{array} ight. $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ 9x+7y=-11; -2x-5y=30 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}9x+7y=-11\-2x-5y=30\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=-\frac{11+7y}{9}\-2x-5y=30\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$-2\left(-\frac{11+7y}{9}ight)-5y=30$$
- step3: Multiply the terms:
  $$\frac{2\left(11+7yight)}{9}-5y=30$$
- step4: Multiply both sides of the equation by LCD:
  $$\left(\frac{2\left(11+7yight)}{9}-5yight)	imes 9=30	imes 9$$
- step5: Simplify the equation:
  $$22-31y=270$$
- step6: Move the constant to the right side:
  $$-31y=270-22$$
- step7: Subtract the numbers:
  $$-31y=248$$
- step8: Change the signs:
  $$31y=-248$$
- step9: Divide both sides:
  $$\frac{31y}{31}=\frac{-248}{31}$$
- step10: Divide the numbers:
  $$y=-8$$
- step11: Substitute the value of $$y:$$
  $$x=-\frac{11+7\left(-8ight)}{9}$$
- step12: Simplify:
  $$x=5$$
- step13: Calculate:
  $$\left\{ \begin{array}{l}x=5\y=-8\end{array}ight.$$
- step14: Check the solution:
  $$\left\{ \begin{array}{l}x=5\y=-8\end{array}ight.$$
- step15: Rewrite:
  $$\left(x,yight) = \left(5,-8ight)$$
The solution to the system of equations is $$ (x,y) = (5,-8) $$.
The solution is $$ x=5 $$ and $$ y=-8 $$.

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