Solve each system of equations by the elimination method. $- 4 x - 7 y = - 16$ $- 5 x + 2 y = 18$
A) $\left( \frac { 152 } { 43 } , - \frac { 94 } { 43 } \right)$
B) $\left( - \frac { 158 } { 43 } , \frac { 8 } { 43 } \right)$
C) $\left( - \frac { 94 } { 43 } , \frac { 152 } { 43 } \right)$
D) $\left( \frac { 152 } { 27 } , - \frac { 94 } { 27 } \right)$
E)no solution

Question

Quizplus · Accepted Answer

To solve the system of equations by elimination, we first multiply each equation by a number that makes the coefficients of $y$ in both equations opposites, so they cancel out when added. Multiplying the first equation by 2 and the second by 7 gives:$$ -8x - 14y = -32 $$$$ -35x + 14y = 126 $$Adding these equations eliminates $y$, resulting in:$$ -43x = 94 $$Solving for $x$ gives $x = \frac{94}{-43} = -\frac{94}{43}$.Substituting $x$ back into one of the original equations to solve for $y$, using the first equation:$$ -4(-\frac{94}{43}) - 7y = -16 $$$$ \frac{376}{43} - 7y = -16 $$$$ -7y = -16 - \frac{376}{43} $$$$ -7y = -\frac{688}{43} $$$$ y = \frac{688}{301} = \frac{152}{43} $$Thus, the solution is $x = -\frac{94}{43}$, $y = \frac{152}{43}$, which corresponds to choice A.

Solve Each System of Equations by the Elimination Method −4x−7y=−16- 4 x - 7 y = - 16−4x−7y=−16

Solve Each System of Equations by the Elimination Method $- 4 x - 7 y = - 16$