Solve the system of linear equations below by the method of elimination, if a single solution exists. $\left\{ \begin{array} { c }
- 9 u - 8 v = - 8 \
9 u + 2 v = 2
\end{array} \right.$
A) $u = 8 \text { and } v = - 2$
B) $u = - 3 \text { and } v = 5$
C) $u = - 6 \text { and } v = 7$
D) $u = 0 \text { and } v = 1$
E)no solution

Question

Solve the system of linear equations below by the method of elimination, if a single solution exists. $\left\{ \begin{array} { c } 
- 9 u - 8 v = - 8 \
9 u + 2 v = 2
\end{array} \right.$
A) $u = 8 \text { and } v = - 2$
B) $u = - 3 \text { and } v = 5$
C) $u = - 6 \text { and } v = 7$
D) $u = 0 \text { and } v = 1$
E)no solution

Quizplus · Accepted Answer

Multiplying the second equation by $4$ we get, $36u+8v=8$. Adding this to the first equation which is $-9u-8v=-8$ gives $27u=0$ which implies $u=0$. Substituting the value of $u$ in any one equation above we get $v=1$. Thus the solution is $(u,v)=(0,1)$. Therefore, the answer is D.

Solve the System of Linear Equations Below by the Method {−9u−8v=−89u+2v=2\left\{ \begin{array} { c } - 9 u - 8 v = - 8 \\9 u + 2 v = 2\end{array} \right.{−9u−8v=−89u+2v=2​

Solve the System of Linear Equations Below by the Method $\left\{ \begin{array} { c } - 9 u - 8 v = - 8 \\9 u + 2 v = 2\end{array} \right.$