To find the solution for the system of linear equations shown in the graph, we need to find the point of intersection of the two lines.
The first line passes through the points (0,0) and (1,3). We can find the equation of this line using the slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
The slope of the line can be found using the two given points:
m = (y2 - y1) / (x2 - x1)
m = (3 - 0) / (1 - 0)
m = 3/1
m = 3
The y-intercept of the line is (0,0), so b = 0.
Therefore, the equation of the first line is:
y = 3x
The second line passes through the points (0,2) and (1,1). We can find the equation of this line using the slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
The slope of the line can be found using the two given points:
m = (y2 - y1) / (x2 - x1)
m = (1 - 2) / (1 - 0)
m = -1/1
m = -1
The y-intercept of the line is (0,2), so b = 2.
Therefore, the equation of the second line is:
y = -x + 2
To find the point of intersection of these two lines, we can set their equations equal to each other:
3x = -x + 2
Solving for x, we get:
4x = 2
x = 1/2
Substituting x=1/2 into either equation, we can find y:
y = 3x
y = 3(1/2)
y = 3/2
Therefore, the point of intersection of the two lines is (1/2, 3/2).
So, the solution for the system of linear equations shown in the graph is:
x = 1/2
y = 3/2
Therefore, the correct response is:
one half comma three halves