$$ 7 \left\{ \begin{array} { l } { 3 x + 2 y = 5 } \ { 5 x - 2 y = 7 } \end{array} ight. $$

Question

$$ 7 \left\{ \begin{array} { l } { 3 x + 2 y = 5 } \ { 5 x - 2 y = 7 } \end{array} ight. $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ 3x+2y=5;5x-2y=7 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}3x+2y=5\5x-2y=7\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=\frac{5-2y}{3}\5x-2y=7\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$5	imes \frac{5-2y}{3}-2y=7$$
- step3: Simplify:
  $$\frac{5\left(5-2yight)}{3}-2y=7$$
- step4: Multiply both sides of the equation by LCD:
  $$\left(\frac{5\left(5-2yight)}{3}-2yight)	imes 3=7	imes 3$$
- step5: Simplify the equation:
  $$25-16y=21$$
- step6: Move the constant to the right side:
  $$-16y=21-25$$
- step7: Subtract the numbers:
  $$-16y=-4$$
- step8: Change the signs:
  $$16y=4$$
- step9: Divide both sides:
  $$\frac{16y}{16}=\frac{4}{16}$$
- step10: Divide the numbers:
  $$y=\frac{1}{4}$$
- step11: Substitute the value of $$y:$$
  $$x=\frac{5-2	imes \frac{1}{4}}{3}$$
- step12: Simplify:
  $$x=\frac{3}{2}$$
- step13: Calculate:
  $$\left\{ \begin{array}{l}x=\frac{3}{2}\y=\frac{1}{4}\end{array}ight.$$
- step14: Check the solution:
  $$\left\{ \begin{array}{l}x=\frac{3}{2}\y=\frac{1}{4}\end{array}ight.$$
- step15: Rewrite:
  $$\left(x,yight) = \left(\frac{3}{2},\frac{1}{4}ight)$$
The solution to the system of equations $$3x+2y=5$$ and $$5x-2y=7$$ is $$x = \frac{3}{2}$$ and $$y = \frac{1}{4}$$ or $$x = 1.5$$ and $$y = 0.25$$.
$$ x = \frac{3}{2}, y = \frac{1}{4} $$

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