Solve the following system of equations graphically on the set of axes below.
y = 2x – 1
x + 2y = 8
Plot two lines by clicking the graph. Click a line to delete it.
Solve the following system of equations graphically on the set of axes below. y = 2x – 1 x + 2y = 8 Plot two lines by clicking the graph. Click a line to delete it
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To solve the system of equations graphically, we will plot each equation on the same set of axes and find the point where the two lines intersect.
1. First Equation: y = 2x – 1
– This is in slope-intercept form (y = mx + b), where the slope (m) is 2 and the y-intercept (b) is -1. So, the first line crosses the y-axis at (0, -1) and rises 2 units for every 1 unit it runs to the right.
2. Second Equation: x + 2y = 8
– We can rearrange this into slope-intercept form. Start by isolating y:
[
2y = -x + 8 \
y = -frac{1}{2}x + 4
]
– Here, the slope is -1/2 and the y-intercept is 4. This line crosses the y-axis at (0, 4) and falls 1 unit for every 2 units it runs to the right.
Plotting the Lines:
– For the first line, plot (0, -1) and another point by choosing x = 1:
[
y = 2(1) – 1 = 1 text{ (point (1, 1))}
]
– For the second