Chapter 6, Problem 1RE

To determine

To calculation: Solve the system of equations: $\begin{array}{c}-5x-3y=-3\\ 2x+y=4\end{array}$

Answer to Problem 1RE

Solution:

The solution of the system is $\underset{\_}{\left(9,-14\right)}$.

Explanation of Solution

Given:

$\begin{array}{c}-5x-3y=-3\\ 2x+y=4\end{array}$

Calculation:

Solve the second equation for y:

$2x+y=4$

Subtract 2x from both sides:

$y=-2x+4$ …...…... (1)

Substitute this expression for y in the first equation and solve for x:

$\begin{array}{c}-5x-3\left(-2x+4\right)=-3\\ -5x+6x-12=-3\\ x=-3+12\\ x=9\end{array}$

Therefore, every solution of the system must have $x=9$. To find the corresponding solution for y, substitute the value $x=9$ in equation (1) and solve for y.

$\begin{array}{c}y=-2x+4\\ y=-2\left(9\right)+4\\ y=-18+4\\ y=-14\end{array}$

Hence, the solution of the system is $\left(9,-14\right)$.