Chapter 11.1, Problem 12AYU

To determine

The solution of the given system of equations.

Answer to Problem 12AYU

$\left(x,y\right)=\left(-2,-5\right)$ is the solution.

Explanation of Solution

Given:

$x-y=3$

$-3x+y=1$

$x=-2,y=-5$

Calculation:

The system of equations is,

$x-y=3$

$-3x+y=1$

From the first equation we get,

$x=3+y$

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

$-3\left(3+y\right)+y=1$

$-9-3y+y=1$

$-2y=1+9$

$-2y=10$

$y=\frac{10}{-2}$

$y=-5$

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

$x-\left(-5\right)=3$

$x+5=3$

$x=3-5$

$x=-2$

Thus the solution is $x=-2,y=-5$.

Therefore the given point $\left(-2,-5\right)$ satisfies the given system of equations and hence is the solution.