Answer:
Plot the following points on the graph:
4x - y = -5: (0, 5), (-5/4, 0)
x + 2y = -8: (0, -4), (-8, 0)
Step-by-step explanation:
4x - y = -5
x + 2y = -8
Solving system graphically involves finding at least 2 pairs of points for each linear equation to plot. Since you have 2 linear equations, then it means that you need at least 4 pairs of coordinates to plot on your graph. The x- and y-intercepts are often used for solving systems of linear equations graphically.
Start by transforming both equations into its slope-intercept form: y = mx + b
4x - y = -5
Subtract 4x from both sides:
4x - 4x - y = - 4x - 5
-y = -4x - 5
Divide both sides by -1, which results into:
y = 4x + 5 (this is your linear equation for 4x - y = -5).
By definition, the y-intercept is the point on the graph where it crosses the y-axis. It is also the value of y when x = 0. The y-coordinate of your y-intercept is 5, which means its coordinates is (0, 5).
The x-intercept is the point on the graph where it crosses the x-axis. It is also the value of x when y = 0.
You could find the <u>x-intercept</u> by setting y = 0:
y = 4x + 5
0 = 4x + 5
Subtract 5 from both sides:
0 - 5 = 4x + 5 - 5
-5 = 4x
Divide both sides by 4:
-5/4 = x
Therefore, the x-intercept = (-5/4, 0).
x + 2y = -8
Do the same process for this equation.
Subtract x from both sides:
x - x + 2y = - x - 8
2y = -x - 8
Divide both sides by 2:
y = - ½x - 4
The y-coordinate of your y-intercept is -4, which means that the y-intercept = (0, -4).
Solve for the x-intercept by setting y = 0:
y = - ½x - 4
0 = - ½x - 4
Add 4 to both sides:
0 + 4 = - ½x - 4 + 4
4 = - ½x
Multiply both sides by -2:
(-2) 4 = (-2) -½x
-8 = x
Therefore, the x-intercept = (-8, 0).
4x - y = -5: (0, 5), (-5/4, 0)
x + 2y = -8: (0, -4), (-8, 0)
Now that you have 2 pairs of coordinates for each linear equation, you can plot these points on the graph. The intersection of these lines will be your solution.
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