10. $$ \begin{array}{l}\frac{y}{2}-\frac{x+3}{4}=\frac{3}{2} \ \frac{y+3}{4}-\frac{x}{2}=\frac{3}{2}\end{array} $$

Question

UpStudy AI · Accepted Answer

Solve the system of equations $$ \frac{y}{2}-\frac{x+3}{4}=\frac{3}{2}; \frac{y+3}{4}-\frac{x}{2}=\frac{3}{2} $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}\frac{y}{2}-\frac{x+3}{4}=\frac{3}{2}\\frac{y+3}{4}-\frac{x}{2}=\frac{3}{2}\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=-9+2y\\frac{y+3}{4}-\frac{x}{2}=\frac{3}{2}\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$\frac{y+3}{4}-\frac{-9+2y}{2}=\frac{3}{2}$$
- step3: Subtract the terms:
  $$\frac{y+3}{4}+\frac{9-2y}{2}=\frac{3}{2}$$
- step4: Multiply both sides of the equation by LCD:
  $$\left(\frac{y+3}{4}+\frac{9-2y}{2}ight)	imes 4=\frac{3}{2}	imes 4$$
- step5: Simplify the equation:
  $$-3y+21=6$$
- step6: Move the constant to the right side:
  $$-3y=6-21$$
- step7: Subtract the numbers:
  $$-3y=-15$$
- step8: Change the signs:
  $$3y=15$$
- step9: Divide both sides:
  $$\frac{3y}{3}=\frac{15}{3}$$
- step10: Divide the numbers:
  $$y=5$$
- step11: Substitute the value of $$y:$$
  $$x=-9+2	imes 5$$
- step12: Simplify:
  $$x=1$$
- step13: Calculate:
  $$\left\{ \begin{array}{l}x=1\y=5\end{array}ight.$$
- step14: Check the solution:
  $$\left\{ \begin{array}{l}x=1\y=5\end{array}ight.$$
- step15: Rewrite:
  $$\left(x,yight) = \left(1,5ight)$$
The solution to the system of equations is $$ (x, y) = (1, 5) $$.
The solution is $$ x = 1 $$ and $$ y = 5 $$.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions