$$ \left. \begin{array} { l } { 12 x + 4 y = 20 \ldots \ldots . . . ( 6 ) } \ { 7 x - 3 y = 19 \ldots \ldots . ( 6 ) } \end{array} ight. $$

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$$ \left. \begin{array} { l } { 12 x + 4 y = 20 \ldots \ldots . . . ( 6 ) } \ { 7 x - 3 y = 19 \ldots \ldots . ( 6 ) } \end{array} ight. $$

UpStudy AI · Accepted Answer

Solve the system of equations $$ 12x+4y=20;7x-3y=19 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}12x+4y=20\7x-3y=19\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=\frac{5-y}{3}\7x-3y=19\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$7	imes \frac{5-y}{3}-3y=19$$
- step3: Simplify:
  $$\frac{7\left(5-yight)}{3}-3y=19$$
- step4: Multiply both sides of the equation by LCD:
  $$\left(\frac{7\left(5-yight)}{3}-3yight)	imes 3=19	imes 3$$
- step5: Simplify the equation:
  $$35-16y=57$$
- step6: Move the constant to the right side:
  $$-16y=57-35$$
- step7: Subtract the numbers:
  $$-16y=22$$
- step8: Change the signs:
  $$16y=-22$$
- step9: Divide both sides:
  $$\frac{16y}{16}=\frac{-22}{16}$$
- step10: Divide the numbers:
  $$y=-\frac{11}{8}$$
- step11: Substitute the value of $$y:$$
  $$x=\frac{5-\left(-\frac{11}{8}ight)}{3}$$
- step12: Substitute back:
  $$x=\frac{5+\frac{11}{8}}{3}$$
- step13: Calculate:
  $$x=\frac{17}{8}$$
- step14: Calculate:
  $$\left\{ \begin{array}{l}x=\frac{17}{8}\y=-\frac{11}{8}\end{array}ight.$$
- step15: Check the solution:
  $$\left\{ \begin{array}{l}x=\frac{17}{8}\y=-\frac{11}{8}\end{array}ight.$$
- step16: Rewrite:
  $$\left(x,yight) = \left(\frac{17}{8},-\frac{11}{8}ight)$$
The solution to the system of equations is $$ x = \frac{17}{8} $$ and $$ y = -\frac{11}{8} $$ or $$ x = 2.125 $$ and $$ y = -1.375 $$.
The solution is $$ x = \frac{17}{8} $$ and $$ y = -\frac{11}{8} $$.

\( \left. \begin{array} { l } { 12 x + 4 y = 20 \ldots \ldots . . . ( 6 ) } \\ { 7 x - 3 y = 19 \ldots \ldots . ( 6 ) } \end{array} \right. \)

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