Use substitution to solve the system of equations.

Ask by Reid Bryant. in the United States

Mar 20,2025

Question

Use substitution to solve the system of equations. $$ \begin{array}{l}5 x+3 y=5 \ x+2 y=-13\end{array} $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ 5x+3y=5;x+2y=-13 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}5x+3y=5\x+2y=-13\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}5x+3y=5\x=-13-2y\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$5\left(-13-2yight)+3y=5$$
- step3: Simplify:
  $$-65-7y=5$$
- step4: Move the constant to the right side:
  $$-7y=5+65$$
- step5: Add the numbers:
  $$-7y=70$$
- step6: Change the signs:
  $$7y=-70$$
- step7: Divide both sides:
  $$\frac{7y}{7}=\frac{-70}{7}$$
- step8: Divide the numbers:
  $$y=-10$$
- step9: Substitute the value of $$y:$$
  $$x=-13-2\left(-10ight)$$
- step10: Calculate:
  $$x=7$$
- step11: Calculate:
  $$\left\{ \begin{array}{l}x=7\y=-10\end{array}ight.$$
- step12: Check the solution:
  $$\left\{ \begin{array}{l}x=7\y=-10\end{array}ight.$$
- step13: Rewrite:
  $$\left(x,yight) = \left(7,-10ight)$$
The solution to the system of equations is $$ (x,y) = (7,-10) $$.
The solution is $$ x=7 $$ and $$ y=-10 $$.

Use substitution to solve the system of equations.

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