Review the graphs of a system of these two linear equations in two variables: y = 4x - 10 and y = - 2x + 8 FInd the solution of system.
The solution of the system of equation is (__).
To find the solution of the system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
First, let's graph each equation to see where they intersect.
For the equation y = 4x - 10, we can plot a few points to create a line:
When x = 0, y = 4(0) - 10 = -10. So we have the point (0, -10).
When x = 2, y = 4(2) - 10 = -2. So we have the point (2, -2).
When x = 4, y = 4(4) - 10 = 6. So we have the point (4, 6).
Plotting these points and drawing a line through them, we get:
Graph 1: Line representing y = 4x - 10
Next, for the equation y = -2x + 8, we can again plot points to create a line:
When x = 0, y = -2(0) + 8 = 8. So we have the point (0, 8).
When x = 2, y = -2(2) + 8 = 4. So we have the point (2, 4).
When x = 4, y = -2(4) + 8 = 0. So we have the point (4, 0).
Plotting these points and drawing a line through them, we get:
Graph 2: Line representing y = -2x + 8
Now, we can see that the two lines intersect at the point (3, 2). This means that the values of x and y that satisfy both equations simultaneously are x = 3 and y = 2.
Therefore, the solution of the system of equations is (3, 2).
Estimate the solution to the system of these linear equations based on the graph.
y = 2x + 3
y = 1/2x + 6
(2, 7)
(7, 2)
(2, -7)
(-2, 7)
Based on the graph of the system of linear equations, it appears that the lines representing the equations y = 2x + 3 and y = 1/2x + 6 intersect at the point (2, 7).
Therefore, the estimate for the solution to the system of equations is (2, 7).
Estimate the solution to the system of these linear equations based on the graph.
y = -x + 6
y = 3x - 2
(__)
Based on the graph of the system of linear equations, it appears that the lines representing the equations y = -x + 6 and y = 3x - 2 intersect at the point (2, 4).
Therefore, the estimate for the solution to the system of equations is (2, 4).
Determine the number of solutions to this system of linear equations:
2x + y = 6
4x + 2y = 8
1
infinite
2
0
To determine the number of solutions to the system of linear equations, we can analyze the system using various methods such as graphing, substitution, or elimination.
Let's use the elimination method:
We can multiply the first equation by 2 to make the coefficients of y in both equations the same:
2(2x + y) = 2(6)
4x + 2y = 12
Now we compare this equation to the second equation:
4x + 2y = 8
Since both equations have the same coefficients for x and y terms, we can subtract the first equation from the second equation:
(4x + 2y) - (4x + 2y) = 8 - 12
0 = -4
This equation simplifies to 0 = -4, which is not a true statement. This means that there are no values of x and y that satisfy both equations simultaneously.
Therefore, the system of linear equations has 0 solutions, or is inconsistent.
Which of the graphs with no solution correctly shows the system of equations
y = 2x + 4 and - 2x + y = 8?
The correct graph that shows the system of equations y = 2x + 4 and -2x + y = 8 with no solution is the one where the two lines are parallel and do not intersect.
In this case, the lines have the same slope of 2, but different y-intercepts. This means that they will never intersect, and there is no solution that satisfies both equations simultaneously.
Therefore, the correct graph with no solution would show two parallel lines.
Which of these graphs shows that the linear system 3x + 2y = 12
and 6x + 4y = 24 has an infinite number of solutions?