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:$$2(x - 2y) = 2(5) \Rightarrow 2x - 4y = 10.$$Now, we have:$$2x - 4y = 10$$$$2x - 3y = 10.$$Subtract the second equation from the first to eliminate $x$:$$(2x - 4y) - (2x - 3y) = 10 - 10$$$$-y = 0 \Rightarrow y = 0.$$Substitute $y = 0$ into the first original equation:$$x - 2(0) = 5 \Rightarrow x = 5.$$Thus, 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 $\left\{ \begin{array} { l l } x - 2 y & = 5 \\2 x - 3 y & = 10\end{array} \right.$