solve the following system of equations by graphing . If the system is inconsistent or the equations are dependent 4x-3y=-12 y=-2x+4
To solve the system of equations by graphing, we first need to graph each equation on the same coordinate plane.
Start with the equation 4x - 3y = -12:
We can rewrite this equation in slope-intercept form, y = mx + b, by isolating y:
4x - 3y = -12
-3y = -4x - 12
y = (4/3)x + 4
Next, graph the equation y = -2x + 4:
This equation is already in slope-intercept form, y = mx + b, where the slope is -2 and the y-intercept is 4.
Now, graph both lines on the same coordinate plane:
Label the first line as Line A and the second line as Line B.
Line A has a slope of (4/3) and a y-intercept of 4. We can plot two points on line A:
- Suppose x = 0,
y = (4/3)(0) + 4
y = 0 + 4
y = 4
So, the first point on line A is (0, 4).
- Suppose y = 0,
0 = (4/3)x + 4
(4/3)x = -4
x = -3
Therefore, the second point on line A is (-3, 0).
Line B has a slope of -2 and a y-intercept of 4. Plot two points on line B:
- Suppose x = 0,
y = -2(0) + 4
y = 0 + 4
y = 4
Hence, the first point on line B is (0, 4).
- Suppose y = 0,
0 = -2x + 4
2x = 4
x = 2
The second point on line B is (2, 0).
After graphing both lines, we can see that they intersect at the point (3, 2). This point is the solution to the system of equations.
The system is consistent (has a solution) and the equations are independent.