# How do you solve the system of equations -2x + 4y = 10  and 3x - 6y = - 15?

Jun 20, 2018

color(crimson)("As equations (1), (2) are the same, we cannot solve for x & y."

#### Explanation:

$- 2 x + 4 y = 10$

$- x + 2 y = 5 , \text{ Eqn (1)}$

$3 x - 6 y = - 15$

$x - 2 y = - 5 , \text{ Eqn (2)}$

As equations (1), (2) are the same, we cannot solve for x & y.

Jun 20, 2018

The system has infinitely many solutions. See explanation.

The system is:

## $\left\{\begin{matrix}- 2 x + 4 y = 10 \\ 3 x - 6 y = - 15\end{matrix}\right.$

We can divide the first equation by $- 2$ and second by $3$ and the equations become the same:

## $x - 2 y = - 5$  (1)

This means that any pair $\left(x , y\right)$ fulfilling the equation (1) is also the solution to the initial system.

Example solutions are then:

(-5;0), (0;2 1/2), (5;5)