Use elimination to solve the system of equations.

Ask by Joseph Erickson. in the United States

Mar 25,2025

Question

Use elimination to solve the system of equations. $$ \begin{array}{l}-2 x+3 y=48 \ 7 x+3 y=21\end{array} $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ -2x+3y=48;7x+3y=21 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}-2x+3y=48\7x+3y=21\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=\frac{-48+3y}{2}\7x+3y=21\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$7	imes \frac{-48+3y}{2}+3y=21$$
- step3: Simplify:
  $$\frac{7\left(-48+3yight)}{2}+3y=21$$
- step4: Multiply both sides of the equation by LCD:
  $$\left(\frac{7\left(-48+3yight)}{2}+3yight)	imes 2=21	imes 2$$
- step5: Simplify the equation:
  $$-336+27y=42$$
- step6: Move the constant to the right side:
  $$27y=42+336$$
- step7: Add the numbers:
  $$27y=378$$
- step8: Divide both sides:
  $$\frac{27y}{27}=\frac{378}{27}$$
- step9: Divide the numbers:
  $$y=14$$
- step10: Substitute the value of $$y:$$
  $$x=\frac{-48+3	imes 14}{2}$$
- step11: Calculate:
  $$x=-3$$
- step12: Calculate:
  $$\left\{ \begin{array}{l}x=-3\y=14\end{array}ight.$$
- step13: Check the solution:
  $$\left\{ \begin{array}{l}x=-3\y=14\end{array}ight.$$
- step14: Rewrite:
  $$\left(x,yight) = \left(-3,14ight)$$
The solution to the system of equations using elimination is $$ (x,y) = (-3,14) $$.
The solution is $$ x = -3 $$ and $$ y = 14 $$.

Use elimination to solve the system of equations.

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