How do you solve the system of equations: x-y=3, x-2y=3?

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Answer 1 · 2015-08-14T11:37:00

The solutions for the system of equations is
$x = 3, y = 0$ $color(blue)(x=3,y=0$

$x - y = 3$ $x-y=3$ , multiplying this equation by $2$ $2$
$2 x - 2 y = 6$ $2x-color(blue)(2y)=6$ .....equation $(1)$ $(1)$

$x - 2 y = 3$ $x-color(blue)(2y)=3$ .......equation $(2)$ $(2)$

Now, we can solve through elimination as we have the term $2 y$ $color(blue)(2y)$ common to both equations.

Subtracting equation $2$ $2$ from equation $1$ $1$

$2x-cancel(color(blue)(2y))=6$
$-x+cancel(color(blue)(2y))=-3$

$color(blue)(x=3$

Now we substitute the value of $x$ in equation $1$ to find $y$
$x-y=3$
$x-3=y$

$color(blue)(y = 0$