Solve, using the substitution method, and check. $\begin{array} { c }
2 x + 3 y = 4 \
5 x - 6 y = - 71
\end{array}$
A) (2, -11)
B) (-6, 5)
C) (4, -3)
D) (7, 6)
E) (-7, 6)

Question

Solve, using the substitution method, and check. $\begin{array} { c } 
2 x + 3 y = 4 \
5 x - 6 y = - 71
\end{array}$
A) (2, -11)
B) (-6, 5)
C) (4, -3)
D) (7, 6)
E) (-7, 6)

Quizplus · Accepted Answer

To solve the system of equations using the substitution method, we first solve one of the equations for one variable in terms of the other. Let's solve the first equation for $x$:$2x + 3y = 4$$2x = 4 - 3y$$x = 2 - \frac{3}{2}y$Now, substitute $x = 2 - \frac{3}{2}y$ into the second equation:$5x - 6y = -71$$5(2 - \frac{3}{2}y) - 6y = -71$$10 - \frac{15}{2}y - 6y = -71$Multiply everything by 2 to clear the fraction:$20 - 15y - 12y = -142$Combine like terms:$20 - 27y = -142$Subtract 20 from both sides:$-27y = -162$Divide by -27:$y = 6$Now, substitute $y = 6$ back into $x = 2 - \frac{3}{2}y$:$x = 2 - \frac{3}{2}(6)$$x = 2 - 9$$x = -7$Therefore, the solution is $x = -7, y = 6$, which corresponds to choice E.

Solve, Using the Substitution Method, and Check 2x+3y=45x−6y=−71\begin{array} { c } 2 x + 3 y = 4 \\5 x - 6 y = - 71\end{array}2x+3y=45x−6y=−71​

Solve, Using the Substitution Method, and Check $\begin{array} { c } 2 x + 3 y = 4 \\5 x - 6 y = - 71\end{array}$