Solve the system of linear equations. $\left\{ \begin{array} { l l }
x - 2 y & = 5 \
2 x - 3 y & = 10
\end{array} \right.$
A) $( 5,10 )$
B) $( 5,5 )$
C) $( 10,5 )$
D) $( 5,0 )$
E) $( 0,5 )$

Question

Solve the system of linear equations.   $\left\{ \begin{array} { l l } 
x - 2 y & = 5 \
2 x - 3 y & = 10
\end{array} \right.$  
A)  $( 5,10 )$
B)  $( 5,5 )$
C)  $( 10,5 )$
D)  $( 5,0 )$
E)  $( 0,5 )$

Quizplus · Accepted Answer

To solve the system of equations, we can use the method of substitution or elimination. Here, using elimination seems straightforward. Multiply the first equation by 2 to align the coefficients of $x$ in both equations:$$2(x - 2y) = 2(5)$$$$2x - 3y = 10$$This gives us:$$2x - 4y = 10$$$$2x - 3y = 10$$Subtracting the second equation from the first gives us:$$-y = 0$$Thus, $y = 0$. Substituting $y = 0$ into the first original equation:$$x - 2(0) = 5$$$$x = 5$$Therefore, the solution is $(5, 0)$.

Solve the System of Linear Equations {x−2y=52x−3y=10\left\{ \begin{array} { l l } x - 2 y & = 5 \\2 x - 3 y & = 10\end{array} \right.{x−2y2x−3y​=5=10​

Solve the System of Linear Equations $\left\{ \begin{array} { l l } x - 2 y & = 5 \\2 x - 3 y & = 10\end{array} \right.$