Find the solution to the system of equations.

$\begin{aligned}

11 x - y & = - 6 \
25 x - 3 y & = - 16
\end{aligned}$

A) $\left( \frac { 1 } { 11 } , - \frac { 1 } { 4 } \right)$

B) $\left( \frac { 1 } { 16 } , \frac { 1 } { 4 } \right)$

C) $\left( - \frac { 1 } { 4 } , \frac { 13 } { 4 } \right)$

D) $\left( \frac { 1 } { 32 } , \frac { 1 } { 4 } \right)$

E) $( 11 , - 11 )$

Question

Find the solution to the system of equations.

$\begin{aligned}

11 x - y & = - 6 \
25 x - 3 y & = - 16
\end{aligned}$

A) $\left( \frac { 1 } { 11 } , - \frac { 1 } { 4 } \right)$

B) $\left( \frac { 1 } { 16 } , \frac { 1 } { 4 } \right)$

C) $\left( - \frac { 1 } { 4 } , \frac { 13 } { 4 } \right)$

D) $\left( \frac { 1 } { 32 } , \frac { 1 } { 4 } \right)$

E) $( 11 , - 11 )$

Quizplus · Accepted Answer

To solve the system of equations, we can use the method of elimination or substitution. Multiplying the first equation by 3 to align the y terms with the second equation gives us:$$33x - 3y = -18$$$$25x - 3y = -16$$Subtracting these equations from each other to eliminate $y$, we get:$$8x = -2$$$$x = -\frac{1}{4}$$Substituting $x = -\frac{1}{4}$ into the first equation:$$11(-\frac{1}{4}) - y = -6$$$$-\frac{11}{4} - y = -6$$$$y = -6 + \frac{11}{4} = -\frac{24}{4} + \frac{11}{4} = -\frac{13}{4}$$Thus, the solution is $x = -\frac{1}{4}, y = \frac{13}{4}$, which corresponds to choice C.

Find the Solution to the System of Equations 11x−y=−625x−3y=−16\begin{aligned}11 x - y & = - 6 \\25 x - 3 y & = - 16\end{aligned}11x−y25x−3y​=−6=−16​

Find the Solution to the System of Equations $\begin{aligned}11 x - y & = - 6 \\25 x - 3 y & = - 16\end{aligned}$