$$ 1 \leftarrow $$ Solve the system of equations by the substitution method. $$ \begin{aligned} y & =\frac{5}{8} x+\frac{5}{8} \ y & =\frac{1}{3} x-2\end{aligned} $$

Question

UpStudy AI · Accepted Answer

Solve the system of equations $$ y=\frac{5}{8}x+\frac{5}{8},y=\frac{1}{3}x-2 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}y=\frac{5}{8}x+\frac{5}{8}\y=\frac{1}{3}x-2\end{array}ight.$$
- step1: Substitute the value of $$y:$$
  $$\frac{5}{8}x+\frac{5}{8}=\frac{1}{3}x-2$$
- step2: Multiply both sides of the equation by LCM:
  $$\left(\frac{5}{8}x+\frac{5}{8}ight)	imes 24=\left(\frac{1}{3}x-2ight)	imes 24$$
- step3: Calculate:
  $$15x+15=\left(\frac{1}{3}x-2ight)	imes 24$$
- step4: Calculate:
  $$15x+15=8x-48$$
- step5: Move the expression to the left side:
  $$15x-8x=-48-15$$
- step6: Add and subtract:
  $$7x=-48-15$$
- step7: Add and subtract:
  $$7x=-63$$
- step8: Divide both sides:
  $$\frac{7x}{7}=\frac{-63}{7}$$
- step9: Divide the numbers:
  $$x=-9$$
- step10: Substitute the value of $$x:$$
  $$y=\frac{5}{8}\left(-9ight)+\frac{5}{8}$$
- step11: Calculate:
  $$y=-5$$
- step12: Calculate:
  $$\left\{ \begin{array}{l}x=-9\y=-5\end{array}ight.$$
- step13: Check the solution:
  $$\left\{ \begin{array}{l}x=-9\y=-5\end{array}ight.$$
- step14: Rewrite:
  $$\left(x,yight) = \left(-9,-5ight)$$
The solution to the system of equations by the substitution method is $$ (x,y) = (-9,-5) $$.
The solution is $$ x = -9 $$ and $$ y = -5 $$.

Solve the system of equations by the substitution method.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions