Solve the following system of equations graphically on the set of axes below.
y, equals, one half, x, plus, 1
y=
2
1
x+1
y, equals, minus, 3, x, minus, 6
y=−3x−6
To solve the system of equations graphically, we need to plot the graphs of both equations on the set of axes.
For the first equation, y = (1/2)x + 1:
- We can start by plotting the y-intercept, which is 1. This means that when x = 0, y = 1.
- Next, we can use the slope of (1/2) to find another point on the line. Since the numerator of the slope is 1, we can move up 1 unit and right 2 units from the y-intercept to find another point on the line.
- Using these two points, we can draw a straight line passing through both points.
For the second equation, y = -3x - 6:
- We can start by plotting the y-intercept, which is -6. This means that when x = 0, y = -6.
- Next, we can use the slope of -3 to find another point on the line. Since the numerator of the slope is -3, we can move down 3 units and right 1 unit from the y-intercept to find another point on the line.
- Using these two points, we can draw a straight line passing through both points.
After plotting both equations on the set of axes, the graphs should intersect at a single point. This point represents the solution to the system of equations.