Solution assignment 09 Linear functions and graphs

Given the following two linear equations with two unknown variables $x$ en $y$ :

$2x-y=-1$
$x+2y=7$

Answer the following questions.

1. The equations represent lines. Calculate their slopes.
2. How can you calculate the coordinates of the intersection point $S$ of both lines?

1. The first equation can be written as:

$l: y=2x+1$

and has the slope $2$ .
The second equation can be written as:

$m: y=-\displaystyle\frac{1}{2}x+\displaystyle\frac{7}{2}$

and has the slope $-\displaystyle\frac{1}{2}$ .
We can calculate the $x$ -coordinate of the intersection point $S$ from:

$2x+1=-\displaystyle\frac{1}{2}x+\displaystyle\frac{7}{2}$
$4x+2=-x+7$
$5x=5$
$x=1$

and so

$y=3$

The coordinates of $S$ are $(1,3)$ .

An alternative calculation.
We could have calculated this result directly from the two previous equations:

$2x-y=-1$
$x+2y=7$

Just multiply the second equation with $2$ :

$2x-y=-1$
$2x+4y=14$

and subtract it from the first equation. Then we get:

$-5y=-15$
$y=3$

and so $x=1$ .