Chapter 6.3, Problem 3P

Solve each system using elimination.

$2x-y=4$

$3x-y=2$

To determine

Solve the system $2x-y=4\text{ and 3}x-y=2$ using elimination method.

Answer to Problem 3P

The solution for the given equations is $x=-2\text{and }y=-8$ .

Explanation of Solution

Given information: The given equations are,

  $\begin{array}{c}2x-y=4\mathrm{....}\left(1\right)\\ \text{3}x-y=2\mathrm{....}\left(2\right)\end{array}$

Calculation: Subtract (1) from (2) gives $x=-2$ .

Substitute $x=-2$ in (1) and simplify,

  $\begin{array}{c}2\left(-2\right)-y=4\mathrm{....}\left(\text{For }x=-2\right)\\ \text{or, }y=-4-4\\ y=-8\end{array}$

Hence the solution for the given equations is $x=-2\text{and }y=-8$ .