solve the sytem of equation by graphing. Then classify the system as consistent or inconsistent and the equation as dependent or independent.
y=-x-11
3x-2y=2
what is the solution of the system of equation.,
All right, that does it. Let me see you try.
Multiply the first equation, every term, by 2
Then add the first equation to the second and watch y disappear so you can solve for x
To solve the system of equations by graphing, you can follow these steps:
Step 1: Graph the first equation: y = -x - 11.
- Choose two values for x, such as x = 0 and x = 5.
- Plug in these values in the equation to find the corresponding y values.
For x = 0, y = -0 - 11 = -11. So, one point on the graph is (0, -11).
For x = 5, y = -5 - 11 = -16. So, the second point on the graph is (5, -16).
- Plot these points and draw a straight line passing through them.
Step 2: Graph the second equation: 3x - 2y = 2.
- Convert it to slope-intercept form (y = mx + b).
3x - 2y = 2
-2y = -3x + 2
y = (3/2)x - 1.
- Choose two values for x, such as x = 0 and x = 5.
- Plug in these values in the equation to find the corresponding y values.
For x = 0, y = (3/2)(0) - 1 = -1. So, one point on the graph is (0, -1).
For x = 5, y = (3/2)(5) - 1 = 6.5. So, the second point on the graph is (5, 6.5).
- Plot these points and draw a straight line passing through them.
Step 3: Analyze the graph.
- Look at the intersection point of the two lines on the graph.
- If the lines intersect at a single point, it means that there is one unique solution, and the system is consistent and independent.
- If the lines do not intersect, it means there is no solution, and the system is inconsistent.
- If the lines are the same (coincide with each other), it means there are infinitely many solutions, and the system is consistent and dependent.
Based on the graph, the lines of the two equations intersect at the point (-4, 7). Therefore, the solution to the system of equations is x = -4 and y = 7.
Since the lines intersect at a single point, the system is consistent. And since the solution is unique, the equations are independent.