What is the solution to this system of equations?

Ask by Barber Perkins. in the United States

Jan 24,2025

Question

What is the solution to this system of equations? $$ \begin{array}{l}y=2-x \ 3 x-2 y=16 \ (4,-2) \ (0,2) \ (5,-3) \ (-4,2)\end{array} $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ y=2-x;3x-2y=16 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}y=2-x\3x-2y=16\end{array}ight.$$
- step1: Substitute the value of $$y:$$
  $$3x-2\left(2-xight)=16$$
- step2: Simplify:
  $$5x-4=16$$
- step3: Move the constant to the right side:
  $$5x=16+4$$
- step4: Add the numbers:
  $$5x=20$$
- step5: Divide both sides:
  $$\frac{5x}{5}=\frac{20}{5}$$
- step6: Divide the numbers:
  $$x=4$$
- step7: Substitute the value of $$x:$$
  $$y=2-4$$
- step8: Simplify:
  $$y=-2$$
- step9: Calculate:
  $$\left\{ \begin{array}{l}x=4\y=-2\end{array}ight.$$
- step10: Check the solution:
  $$\left\{ \begin{array}{l}x=4\y=-2\end{array}ight.$$
- step11: Rewrite:
  $$\left(x,yight) = \left(4,-2ight)$$
The solution to the system of equations is $$ (x,y) = (4,-2) $$.
The solution is $$ (4, -2) $$.

What is the solution to this system of equations?

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