Question

olve the following system of equations graphically on the set of axes below.
y, equals, one fifth, x, plus, 1
y=
5
1
​
x+1
y, equals, minus, x, plus, 7
y=−x+7

Answer 1

The two equations are:
1. y = (1/5)x + 1
2. y = -x + 7

To graph these two equations, start by plotting the y-intercepts:
1. For y = (1/5)x + 1, the y-intercept is 1, so plot the point (0, 1).
2. For y = -x + 7, the y-intercept is 7, so plot the point (0, 7).

Next, find a couple more points for each line to sketch the graphs. For y = (1/5)x + 1, choose x = 5 and x = -5 to find corresponding y values:
1. When x = 5: y = (1/5)(5) + 1 = 2
2. When x = -5: y = (1/5)(-5) + 1 = 0
So, plot the points (5, 2) and (-5, 0) for the first equation.

For y = -x + 7, when x = 5: y = -5 + 7 = 2
When x = -5: y = 5 + 7 = 12
So, plot the points (5, 2) and (-5, 12) for the second equation.

Connect the points to sketch the graphs of both equations on the same set of axes. The intersection point of the two lines is the solution to the system of equations.

The graph will have two lines intersecting at the point (5, 2).