Estimate the solution to the system of these linear equations based on the graph.
y = 2x + 3
У = 1/2x + 6
11 answers
Based on the graph of the two linear equations, the point of intersection appears to be around (1, 5). This would be the estimated solution to the system of equations y = 2x + 3 and y = 1/2x + 6.
Wrong
Let's find the exact solution to the system of equations y = 2x + 3 and y = 1/2x + 6.
Since both equations are equal to y, we can set them equal to each other:
2x + 3 = 1/2x + 6
Now, let's solve for x:
2x - 1/2x = 6 - 3
(4/2)x - (1/2)x = 3
(3/2)x = 3
x = 3/(3/2)
x = 3 * 2/3
x = 2
Now that we have x = 2, we can substitute this back into one of the equations to find y. Let's use the equation y = 2x + 3:
y = 2(2) + 3
y = 4 + 3
y = 7
Therefore, the solution to the system of equations y = 2x + 3 and y = 1/2x + 6 is x = 2 and y = 7.
Since both equations are equal to y, we can set them equal to each other:
2x + 3 = 1/2x + 6
Now, let's solve for x:
2x - 1/2x = 6 - 3
(4/2)x - (1/2)x = 3
(3/2)x = 3
x = 3/(3/2)
x = 3 * 2/3
x = 2
Now that we have x = 2, we can substitute this back into one of the equations to find y. Let's use the equation y = 2x + 3:
y = 2(2) + 3
y = 4 + 3
y = 7
Therefore, the solution to the system of equations y = 2x + 3 and y = 1/2x + 6 is x = 2 and y = 7.
A) (2, -7)
B) (-2,7)
C) (7, 2)
D) (2, 7)
B) (-2,7)
C) (7, 2)
D) (2, 7)
Let's check the solution of the system of equations y = 2x + 3 and y = 1/2x + 6 by substituting it into the equations.
For the point (2, 7):
y = 2(2) + 3
y = 4 + 3
y = 7
y = 1/2(2) + 6
y = 1 + 6
y = 7
So, the point (2, 7) satisfies both equations. Therefore, the correct answer is D) (2, 7).
For the point (2, 7):
y = 2(2) + 3
y = 4 + 3
y = 7
y = 1/2(2) + 6
y = 1 + 6
y = 7
So, the point (2, 7) satisfies both equations. Therefore, the correct answer is D) (2, 7).
Estimate the solution to the system of these linear equations based on the graph.
У =-х +6
У = 3Х -2
У =-х +6
У = 3Х -2
Based on the graph of the two linear equations y = -x + 6 and y = 3x - 2, the point of intersection appears to be around (2, 4). So, the estimated solution to the system of equations would be x = 2 and y = 4.
Determine the number of solutions to this system of linear equations:
2x + y=6
1x + 2y = 8
2x + y=6
1x + 2y = 8
To determine the number of solutions to this system of linear equations, we need to check if the two equations are consistent and whether they intersect at a single point, have no solution, or have infinitely many solutions.
Let's rearrange the equations into slope-intercept form:
1. 2x + y = 6 becomes y = -2x + 6
2. x + 2y = 8 becomes y = -1/2x + 4
The equations are consistent and have different slopes, indicating that the lines intersect at a single point. Therefore, this system of linear equations has exactly one solution.
Let's rearrange the equations into slope-intercept form:
1. 2x + y = 6 becomes y = -2x + 6
2. x + 2y = 8 becomes y = -1/2x + 4
The equations are consistent and have different slopes, indicating that the lines intersect at a single point. Therefore, this system of linear equations has exactly one solution.
Solve the system of equations.
4х - 8y=-36
4х - 8y=-36
It seems that you have provided only one equation (4x - 8y = -36). In order to solve a system of equations, we need at least two equations. If you have another equation to provide, please include it so we can solve the system for you.
1 answer