Chapter 11.1, Problem 7AYU

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

$x\text{ = 2},y\text{ = }-1;\left(2,-1\right)$

To determine

The solution of the given system of equations.

Answer to Problem 7AYU

$\left(x,y\right)=\left(2,-1\right)$ is the solution.

Explanation of Solution

Given:

$2x-y=5$

$5x+2y=8$

$x=2,y=-1$

Calculation:

The system of equations is,

$2x-y=5$

$5x+2y=8$

From the first equation we get,

$y=2x-5$

Substituting this value of $y$ in the second equation we get,

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

$5x+4x-10=8$

$9x-10=8$

$9x-10+10=8+10$

$9x=18$

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

$x=2$

Substituting this value of $x$ in the first equation we get,

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

$4-y=5$

$4-y+y=5+y$

$4=5+y$

$-5+4=-5+5+y$

$-1=y$

$y=-1$

Thus the solution is $x=2,y=-1$.

Therefore the given point $\left(2,-1\right)$ satisfies the given system of equations and hence is the solution.