# How do you graph each system and determine the number of solutions of y=2x-3, y=x+4?

Jan 11, 2017

Only one solution $x = 7$ and $y = 11$.

#### Explanation:

WE can draw the graph using slope-intercept form of equation, which is $y = m x + c$, where $m$ is slope and $c$ is the intercept formed by the line graph (as they are linear equations in $x$ and $y$, they form a line) on $y$=axis.

The equation $y = 2 x - 3$ is a line with slope $2$ and $- 3$ is the intercept on $y$=axis. And the equation $y = x + 4$ is a line with slope $1$ and $4$ is the intercept on $y$=axis. Hence they form the graph as follows.
graph{(y-2x+3)(y-x-4)=0 [-19.25, 20.75, -6.32, 13.68]}

As the slopes are different, the lines intersect (lines are either parallel, when their slopes are equal, or they intersect at one point) and from graph, we observe that they intersect at $\left(7 , 11\right)$

Note: In case you have difficulty in drawing graph with given $y$-intercept and slope, one can also try finding $x$ intercept by putting $y = 0$ in the equation.

In first equation $y = 2 x - 3$, if $y = 0$, $x = \frac{3}{2}$ i.e. it passes through $\left(- \frac{3}{2} , 0\right)$. And as $y$-intercept is $- 3$, it passes through $\left(0 , - 3\right)$ and joining these points will give us graph for the first equation.

For second equation, $y$-intercept is $4$ and hence it passes through $\left(0 , 4\right)$ and putting $y = 0$, we get $x$-intercept as $- 4$ and hence the line passes through points $\left(0 , 4\right)$ and $\left(- 4 , 0\right)$ and joining these points will give us graph for other equation.