Solve the system by graphing $$ \begin{array}{l}y=\frac{1}{2} x-2 \ y=4 x+5\end{array} $$

Question

UpStudy AI · Accepted Answer

Solve the system of equations $$ y=\frac{1}{2}x-2;y=4x+5 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}y=\frac{1}{2}x-2\y=4x+5\end{array}ight.$$
- step1: Substitute the value of $$y:$$
  $$\frac{1}{2}x-2=4x+5$$
- step2: Multiply both sides of the equation by LCM:
  $$\left(\frac{1}{2}x-2ight)	imes 2=\left(4x+5ight)	imes 2$$
- step3: Calculate:
  $$x-4=\left(4x+5ight)	imes 2$$
- step4: Calculate:
  $$x-4=8x+10$$
- step5: Move the expression to the left side:
  $$x-8x=10+4$$
- step6: Add and subtract:
  $$-7x=10+4$$
- step7: Add and subtract:
  $$-7x=14$$
- step8: Change the signs:
  $$7x=-14$$
- step9: Divide both sides:
  $$\frac{7x}{7}=\frac{-14}{7}$$
- step10: Divide the numbers:
  $$x=-2$$
- step11: Substitute the value of $$x:$$
  $$y=\frac{1}{2}\left(-2ight)-2$$
- step12: Simplify:
  $$y=-3$$
- step13: Calculate:
  $$\left\{ \begin{array}{l}x=-2\y=-3\end{array}ight.$$
- step14: Check the solution:
  $$\left\{ \begin{array}{l}x=-2\y=-3\end{array}ight.$$
- step15: Rewrite:
  $$\left(x,yight) = \left(-2,-3ight)$$
The solution to the system of equations $$y=\frac{1}{2}x-2$$ and $$y=4x+5$$ is $$x=-2$$ and $$y=-3$$.
The solution is $$ x = -2 $$ and $$ y = -3 $$.

Solve the system by graphing

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions