QUESTION 15 - 5 POINTS
Determine the solution of the given system of equations.

Ask by Sanders Bowen. in the United States

Nov 30,2024

Question

QUESTION 15 - 5 POINTS Determine the solution of the given system of equations. $$ \left\{\begin{array}{ll}-x+y & =-5 \ -4 x-5 y & =7\end{array}\right. $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ -x+y=-5;-4x-5y=7 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}-x+y=-5\-4x-5y=7\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=5+y\-4x-5y=7\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$-4\left(5+yight)-5y=7$$
- step3: Simplify:
  $$-20-9y=7$$
- step4: Move the constant to the right side:
  $$-9y=7+20$$
- step5: Add the numbers:
  $$-9y=27$$
- step6: Change the signs:
  $$9y=-27$$
- step7: Divide both sides:
  $$\frac{9y}{9}=\frac{-27}{9}$$
- step8: Divide the numbers:
  $$y=-3$$
- step9: Substitute the value of $$y:$$
  $$x=5-3$$
- step10: Simplify:
  $$x=2$$
- step11: Calculate:
  $$\left\{ \begin{array}{l}x=2\y=-3\end{array}ight.$$
- step12: Check the solution:
  $$\left\{ \begin{array}{l}x=2\y=-3\end{array}ight.$$
- step13: Rewrite:
  $$\left(x,yight) = \left(2,-3ight)$$
The solution to the given system of equations is $$ (x, y) = (2, -3) $$.
The solution is $$ (x, y) = (2, -3) $$.

QUESTION 15 - 5 POINTS
Determine the solution of the given system of equations.

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