To solve the system of equations graphically, we can plot the two linear equations on a graph and find the point of intersection.
First, let's plot the equation y = -2x - 1. We can start by plotting a few points on the graph and then connecting them to form a line:
When x = 0, y = -2(0) - 1 = -1. So one point on the line is (0, -1).
When x = 1, y = -2(1) - 1 = -3. So another point on the line is (1, -3).
When x = -1, y = -2(-1) - 1 = 1. So another point on the line is (-1, 1).
Plotting these three points on the graph and connecting them with a line, we get:
{{{graph(400,400,-5,5,-5,5,-2x-1)}}}
Next, let's plot the equation 3x - y = -7. To plot this line, we can again choose a few values for x and find the corresponding y-values:
When x = 0, 3(0) - y = -7, so y = 7. One point on the line is (0, 7).
When x = 1, 3(1) - y = -7, so y = 10. Another point on the line is (1, 10).
When x = -1, 3(-1) - y = -7, so y = -4. Another point on the line is (-1, -4).
Plotting these three points on the graph and connecting them with a line, we get:
{{{graph(400,400,-5,5,-5,5,-2x-1,3x+7)}}}
The point of intersection of these two lines is approximately (2, -5).
Therefore, the solution to the system of equations is x = 2 and y = -5.
Solve the system of equations graphically. y=−2x−1 3x - y =−7
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