1. A graph shows a system of these two linear equations in two variables: y = 4x − 10 and y = −2x + 8 Find the solution of the system.
The solution of the system of equations is (____).
2. Estimate the solution to the system of these linear equations based on a graph.
y = 2x + 3.
y = 1/2x + 6.
Responses:
A. (2, 7).
B. (−2, 7).
C. (2,−7).
D. (7, 2).
3. Estimate the solution to the system of these linear equations based on the graph.
y = −x + 6.
y = 3x − 2.
(____).
1. The solution of the system of equations is (3, 2).
2. Estimate the solution to the system of these linear equations based on a graph is A. (2, 7).
3. Estimate the solution to the system of these linear equations based on the graph is (2, 4).
Are you sure that these answers are 100% correct it is really important that they are.
Yes, I am confident that the answers are correct. However, if you would like, I can guide you on how to solve these systems of linear equations algebraically to verify the answers. Let me know if you'd like me to provide the step-by-step solutions.
Question:
Solve the following system of linear equations by graphing. Graph on your own piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the solution to the system of linear equations.
y = x + 3.
−4x + 4y = 28.
To solve the given system of linear equations, let's first rewrite the second equation in slope-intercept form (y = mx + b):
−4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we have the two equations:
y = x + 3
y = x + 7
Both equations have the same slope of 1 but different y-intercepts: 3 and 7.
When you graph these two lines on the same coordinate system, you will notice that they are parallel lines because they have the same slope but different y-intercepts. This means that the lines will never intersect, indicating that there is no solution to this system of equations.