System of Equations: y=-x+2 & (I) y=2x-1 & (II)
Solution: (1,1)
Practice makes perfect
We want to write the system of linear equations that is represented by a graph and then find its solution. We will do these things one at a time. First, let's take a look at the given graph.
We can use the points marked on the coordinate plane to find the equations of both lines in slope-intercept form. Let's start with the first line.
From the graph, we can see that the rise of the red line is -2 and the run is 2. Let's use this information to find the slope of the red line.
m=-2/2= -1
We found that the slope of the first line is -1. Now, notice that the red line crosses the y-axis at the point (0, 2). We now have enough information to write the equation of the first line in the slope-intercept form.
y= -1x+ 2 ⇕ y=- x+2
Now we will do the same with the second line. Let's take a look at the graph again.
As we can see from the graph, the rise of the second line is 4 and the run is 2. Using this information we will write the slope of the blue line.
m=4/2= 2
We found that the slope of the blue line is 2. Next, let's focus on y-intercept. The blue line crosses the y-axis at the point (0,-1). We can now write the equation of the second line.
y= 2x+( -1) ⇕ y=2x-1
Now we will combine the two equations we found into one system of equations.
y=-x+2 & (I) y=2x-1 & (II)
Next, let's find the solution to this system. Recall that the solution to a system of linear equations is the point of intersection of the graphs of the equations.
The graphs appear to intersect at the point (1,1). This means that the solution to the system is (1,1).
