Solve the system by the substitution method.

Select the correct choice below and, if necessary, fill in the answer box to complete your
A. The solution set is . (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.

Ask by Pope Bradley. in the United States

Mar 25,2025

Question

Solve the system by the substitution method.

Select the correct choice below and, if necessary, fill in the answer box to complete your
A. The solution set is . (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.

Ask by Pope Bradley. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

Solve the system of equations $$ x-2y=4;y=3x-22 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}x-2y=4\y=3x-22\end{array}ight.$$
- step1: Substitute the value of $$y:$$
  $$x-2\left(3x-22ight)=4$$
- step2: Simplify:
  $$-5x+44=4$$
- step3: Move the constant to the right side:
  $$-5x=4-44$$
- step4: Subtract the numbers:
  $$-5x=-40$$
- step5: Change the signs:
  $$5x=40$$
- step6: Divide both sides:
  $$\frac{5x}{5}=\frac{40}{5}$$
- step7: Divide the numbers:
  $$x=8$$
- step8: Substitute the value of $$x:$$
  $$y=3	imes 8-22$$
- step9: Calculate:
  $$y=2$$
- step10: Calculate:
  $$\left\{ \begin{array}{l}x=8\y=2\end{array}ight.$$
- step11: Check the solution:
  $$\left\{ \begin{array}{l}x=8\y=2\end{array}ight.$$
- step12: Rewrite:
  $$\left(x,yight) = \left(8,2ight)$$
The solution to the system of equations by the substitution method is $$ (x, y) = (8, 2) $$.

Therefore, the correct choice is:
A. The solution set is $$ (8, 2) $$.
The solution is $$ (8, 2) $$.

Solve the system by the substitution method.

Select the correct choice below and, if necessary, fill in the answer box to complete your
A. The solution set is . (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.

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Solve the system by the substitution method. Select the correct choice below and, if necessary, fill in the answer box to complete your A. The solution set is . (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

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Solve the system by the substitution method.

Select the correct choice below and, if necessary, fill in the answer box to complete your
A. The solution set is . (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.