Question
Solve the system by substitution.

Ask by Cross Sandoval. in the United States

Jan 21,2025

Question

Question Solve the system by substitution. $$ \begin{aligned} x & =-4 y-15 \ 2 x+10 y & =8\end{aligned} $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ x=-4y-15;2x+10y=8 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}x=-4y-15\2x+10y=8\end{array}ight.$$
- step1: Substitute the value of $$x:$$
  $$2\left(-4y-15ight)+10y=8$$
- step2: Simplify:
  $$2y-30=8$$
- step3: Move the constant to the right side:
  $$2y=8+30$$
- step4: Add the numbers:
  $$2y=38$$
- step5: Divide both sides:
  $$\frac{2y}{2}=\frac{38}{2}$$
- step6: Divide the numbers:
  $$y=19$$
- step7: Substitute the value of $$y:$$
  $$x=-4	imes 19-15$$
- step8: Simplify:
  $$x=-91$$
- step9: Calculate:
  $$\left\{ \begin{array}{l}x=-91\y=19\end{array}ight.$$
- step10: Check the solution:
  $$\left\{ \begin{array}{l}x=-91\y=19\end{array}ight.$$
- step11: Rewrite:
  $$\left(x,yight) = \left(-91,19ight)$$
The solution to the system of equations by substitution is $$ (x,y) = (-91,19) $$.
The solution is $$ x = -91 $$ and $$ y = 19 $$.

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Solve the system by substitution.

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