$$ -4 x+5 y=8 $$ and $$ 3 x-2 y=1 $$

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Solve the system of equations $$ -4x+5y=8;3x-2y=1 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}-4x+5y=8\3x-2y=1\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=\frac{-8+5y}{4}\3x-2y=1\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$3	imes \frac{-8+5y}{4}-2y=1$$
- step3: Simplify:
  $$\frac{3\left(-8+5yight)}{4}-2y=1$$
- step4: Multiply both sides of the equation by LCD:
  $$\left(\frac{3\left(-8+5yight)}{4}-2yight)	imes 4=1	imes 4$$
- step5: Simplify the equation:
  $$-24+7y=4$$
- step6: Move the constant to the right side:
  $$7y=4+24$$
- step7: Add the numbers:
  $$7y=28$$
- step8: Divide both sides:
  $$\frac{7y}{7}=\frac{28}{7}$$
- step9: Divide the numbers:
  $$y=4$$
- step10: Substitute the value of $$y:$$
  $$x=\frac{-8+5	imes 4}{4}$$
- step11: Calculate:
  $$x=3$$
- step12: Calculate:
  $$\left\{ \begin{array}{l}x=3\y=4\end{array}ight.$$
- step13: Check the solution:
  $$\left\{ \begin{array}{l}x=3\y=4\end{array}ight.$$
- step14: Rewrite:
  $$\left(x,yight) = \left(3,4ight)$$
The solution to the system of equations $$ -4x+5y=8 $$ and $$ 3x-2y=1 $$ is $$ (x,y) = (3,4) $$.
$$ (x,y) = (3,4) $$

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