Solve using the substitution method. Use a graphing calculator to check the answer. $$ \begin{array}{l}x-3 y=14, \ x=y+6\end{array} $$ Aelect the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer. Type an ordered pair, using integers or fractions.) B. There are infinitely many solutions in the form ( $$ x, \square $$. (Simplify your answer.) C. There is no solution.

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The solution is (2, -4). Solve the system of equations $$ x-3y=14;x=y+6 $$. Solve the system of equations by following steps: - step0: Solve using the substitution method: $$\left\{ \begin{array}{l}x-3y=14\x=y+6\end{array}ight.$$ - step1: Substitute the value of $$x:$$ $$y+6-3y=14$$ - step2: Subtract the terms: $$-2y+6=14$$ - step3: Move the constant to the right side: $$-2y=14-6$$ - step4: Subtract the numbers: $$-2y=8$$ - step5: Change the signs: $$2y=-8$$ - step6: Divide both sides: $$\frac{2y}{2}=\frac{-8}{2}$$ - step7: Divide the numbers: $$y=-4$$ - step8: Substitute the value of $$y:$$ $$x=-4+6$$ - step9: Simplify: $$x=2$$ - step10: Calculate: $$\left\{ \begin{array}{l}x=2\y=-4\end{array}ight.$$ - step11: Check the solution: $$\left\{ \begin{array}{l}x=2\y=-4\end{array}ight.$$ - step12: Rewrite: $$\left(x,yight) = \left(2,-4ight)$$ The solution to the system of equations using the substitution method is $$ (x, y) = (2, -4) $$. To check the answer using a graphing calculator, you can plot the two equations $$ x-3y=14 $$ and $$ x=y+6 $$ and see if they intersect at the point (2, -4).

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