Chapter 11, Problem 1RE

In Problems $1-10$, solve each system of equations using the method of substituting or the method of elimination. If the system has no solution, state that it is inconsistent .

$\{\begin{array}{c}2x-y=5\\ 5x+2y=8\end{array}$

To determine

The solution of the system $\{\begin{array}{l}2x-y=5\\ 5x+2y=8\end{array}$ using the method of substitution or method of elimination.

Answer to Problem 1RE

Solution:

The solution of the system $\{\begin{array}{l}2x-y=5\\ 5x+2y=8\end{array}$ is $x=2,y=-1$ or $\left(2,-1\right)$.

Explanation of Solution

Given information:

The system, $\{\begin{array}{l}2x-y=5\\ 5x+2y=8\end{array}$

Explanation:

To solve the system equations by using substitution method,

$2x-y=5$… (1)

$5x+2y=8$… (2)

From equation (1),

$\Rightarrow y=2x-5$

Substitute $y=2x-5$ in the equation (2),

$\Rightarrow 5x+2\left(2x-5\right)=8$

$\Rightarrow 5x+4x-10=8$

$\Rightarrow 9x=18$

$\Rightarrow x=\frac{18}{9}$

$\Rightarrow x=2$… (4)

From equation (4),

$\Rightarrow y=2x-5$

Substitute $x=2$ in the equation $y=2x-5$,

$\Rightarrow y=2\left(2\right)-5$

$\Rightarrow y=-1$

Therefore, the solutions of the system $\{\begin{array}{l}2x-y=5\\ 5x+2y=8\end{array}$ is $x=2,y=-1$ or $\left(2,-1\right)$.