The slope of the given equation y = -2x - 8 is -2. To have infinitely many solutions, the other equation must either be identical or a multiple of the given equation.
We can quickly eliminate option D as it simplifies to y = 2x - 8, which has a different slope.
Option A is the inverse of the given equation, which means it will intersect at one point and not have infinitely many solutions.
Option B has slope -2 and y-intercept of -16, so it is a multiple of the given equation and will have infinitely many solutions.
Option C has slope -2 and y-intercept of -8, which means it is parallel to the given equation and will intersect at one point and not have infinitely many solutions.
Therefore, the correct answer is y = -2(x-8).
The graphed line shown below is y = negative 2 x minus 8.
On a coordinate plane, a line goes through (negative 4, 0) and (negative 2, negative 4).
Which equation, when graphed with the given equation, will form a system that has infinitely many solutions?
y = negative (2 x + 8)
y = negative 2 (x minus 8)
y = negative 2 (x minus 4)
y = negative (negative 2 x + 8)
14 answers
Nita graphed the system of equations on the graph below.
y = negative 3 (x + 2). Y = negative 3 x minus 6.
On a coordinate plane, a line goes through (negative 2, 0) and (negative 1, negative 3).
Which explains why there is only one line?
Each has a slope of –3 and a y-intercept of –6, so the system has infinitely many solutions.
Each has a slope of –3 and a y-intercept of –6, so the system has no solution.
Each has a slope of –3, but one has a y-intercept of 2 and the other has a y-intercept of –6. So, the system has infinitely many solutions.
Each has a slope of –3, but one has a y-intercept of 2 and the other has a y-intercept of –6. So, the system has no solution.
y = negative 3 (x + 2). Y = negative 3 x minus 6.
On a coordinate plane, a line goes through (negative 2, 0) and (negative 1, negative 3).
Which explains why there is only one line?
Each has a slope of –3 and a y-intercept of –6, so the system has infinitely many solutions.
Each has a slope of –3 and a y-intercept of –6, so the system has no solution.
Each has a slope of –3, but one has a y-intercept of 2 and the other has a y-intercept of –6. So, the system has infinitely many solutions.
Each has a slope of –3, but one has a y-intercept of 2 and the other has a y-intercept of –6. So, the system has no solution.
The given system of equations is y = -3(x+2) and y = -3x-6.
We can see that both equations have the same slope of -3, which means they are parallel lines. Parallel lines do not intersect, so the system has no common solution.
Therefore, the correct answer is: Each has a slope of –3 and a y-intercept of –6, so the system has no solution.
We can see that both equations have the same slope of -3, which means they are parallel lines. Parallel lines do not intersect, so the system has no common solution.
Therefore, the correct answer is: Each has a slope of –3 and a y-intercept of –6, so the system has no solution.
A system of equations is given below.
y = negative 3 x + 6 and y = 6 minus 3 x
Which of the following statements best describes the two lines?
They have different slopes and different y-intercepts, so they have no solution.
They have different slopes and different y-intercepts, so they have one solution.
They have the same slope and the same y-intercept, so they have no solution.
They have the same slope and the same y-intercept, so they have infinitely many solutions.
y = negative 3 x + 6 and y = 6 minus 3 x
Which of the following statements best describes the two lines?
They have different slopes and different y-intercepts, so they have no solution.
They have different slopes and different y-intercepts, so they have one solution.
They have the same slope and the same y-intercept, so they have no solution.
They have the same slope and the same y-intercept, so they have infinitely many solutions.
The given system of equations is y = -3x + 6 and y = 6 - 3x.
We can see that both equations have the same slope of -3 and different y-intercepts of 6 and 6, respectively. When the slopes are the same and the y-intercepts are different, the lines are parallel and do not intersect, so there is no solution.
Therefore, the correct answer is: They have the same slope and the same y-intercept, so they have no solution.
We can see that both equations have the same slope of -3 and different y-intercepts of 6 and 6, respectively. When the slopes are the same and the y-intercepts are different, the lines are parallel and do not intersect, so there is no solution.
Therefore, the correct answer is: They have the same slope and the same y-intercept, so they have no solution.
How many solutions does this system have?
2 x minus 4 y = 8. x + y = 7.
no solutions
one unique solution
two solutions
an infinite number of solutions
2 x minus 4 y = 8. x + y = 7.
no solutions
one unique solution
two solutions
an infinite number of solutions
We can solve this system of equations using either substitution or elimination.
Using elimination:
We multiply the second equation by 2 to get 2x + 2y = 14.
We subtract the first equation from the second to get 6y = 6, or y = 1.
We substitute y = 1 into the second equation to get x + 1 = 7, or x = 6.
Therefore, the system has one unique solution.
The answer is: one unique solution.
Using elimination:
We multiply the second equation by 2 to get 2x + 2y = 14.
We subtract the first equation from the second to get 6y = 6, or y = 1.
We substitute y = 1 into the second equation to get x + 1 = 7, or x = 6.
Therefore, the system has one unique solution.
The answer is: one unique solution.
Serina wants to solve the following system of equations in the most efficient way.
2 x + 3 y = 18. x + 7 y = 31.
She plans to solve for x in the first equation as her first step since both 2 and 3 can be divided into 18. Why is Serina mistaken?
Serina should have solved for x in the second equation because it has a coefficient of 1.
Serina should have solved for y in the first equation because dividing by 3 instead of by 2 would give a smaller number in the solution.
Serina should have solved for y in the second equation because it has the largest coefficient.
Serina should have solved for y in the first equation because the division step will be easier since 18 is divisible by 3.
2 x + 3 y = 18. x + 7 y = 31.
She plans to solve for x in the first equation as her first step since both 2 and 3 can be divided into 18. Why is Serina mistaken?
Serina should have solved for x in the second equation because it has a coefficient of 1.
Serina should have solved for y in the first equation because dividing by 3 instead of by 2 would give a smaller number in the solution.
Serina should have solved for y in the second equation because it has the largest coefficient.
Serina should have solved for y in the first equation because the division step will be easier since 18 is divisible by 3.
Serina is mistaken because dividing by 2 in the first equation will make the coefficient of y in the resulting equation a fraction with a denominator of 2, which means that she will have to use fractions to solve for y. On the other hand, in the second equation, the coefficient of x is already 1, which makes it easier to solve for x.
Therefore, the correct answer is: Serina should have solved for x in the second equation because it has a coefficient of 1.
Therefore, the correct answer is: Serina should have solved for x in the second equation because it has a coefficient of 1.
What is the solution to the system of equations below?
y = one-half x + 6 and y = negative three-fourths x minus 4
(3, 9)
(8, 12)
(12, 8)
(9, 3)
y = one-half x + 6 and y = negative three-fourths x minus 4
(3, 9)
(8, 12)
(12, 8)
(9, 3)
Since both equations are set equal to y, we can set them equal to each other to find the value of x.
one-half x + 6 = negative three-fourths x - 4
Multiplying by 4 to eliminate the fractions, we get:
2x + 24 = -3x - 16
Adding 3x to both sides, we get:
5x + 24 = -16
Subtracting 24 from both sides, we get:
5x = -40
Dividing by 5, we get:
x = -8
Now that we know x = -8, we can substitute this value into either equation to find y.
y = one-half (-8) + 6 = 2
Therefore, the solution to the system of equations is (-8, 2).
The answer is not one of the given options.
one-half x + 6 = negative three-fourths x - 4
Multiplying by 4 to eliminate the fractions, we get:
2x + 24 = -3x - 16
Adding 3x to both sides, we get:
5x + 24 = -16
Subtracting 24 from both sides, we get:
5x = -40
Dividing by 5, we get:
x = -8
Now that we know x = -8, we can substitute this value into either equation to find y.
y = one-half (-8) + 6 = 2
Therefore, the solution to the system of equations is (-8, 2).
The answer is not one of the given options.
Which system of equations shows a solution of (0.5, –1)?
On a coordinate plane, 2 lines intersect at (0.5, negative 1).
On a coordinate plane, 2 lines intersect at (negative 0.5, negative 1).
On a coordinate plane, 2 lines intersect at (negative 0.5, 1).
On a coordinate plane, 2 lines intersect at (0.5, 1).
On a coordinate plane, 2 lines intersect at (0.5, negative 1).
On a coordinate plane, 2 lines intersect at (negative 0.5, negative 1).
On a coordinate plane, 2 lines intersect at (negative 0.5, 1).
On a coordinate plane, 2 lines intersect at (0.5, 1).
To check which system of equations shows a solution of (0.5, -1), we can substitute x = 0.5 and y = -1 into each equation and see if they are true.
Option A: On a coordinate plane, 2 lines intersect at (0.5, negative 1).
We don't have any equations to work with, so we cannot check this option.
Option B: On a coordinate plane, 2 lines intersect at (negative 0.5, negative 1).
Again, we don't have any equations to work with, so we cannot check this option.
Option C: On a coordinate plane, 2 lines intersect at (negative 0.5, 1).
The x-coordinate is not 0.5, so this is not a solution. Eliminate this option.
Option D: On a coordinate plane, 2 lines intersect at (0.5, 1).
Let's write the equations of the two lines passing through (0.5, 1) and (-0.5, -1) respectively and then substitute (0.5, -1) in them:
Line 1: Passing through (0.5, 1) with slope (1 - (-1))/(0.5 - (-0.5)) = 2/1 = 2, we can write the point-slope form of the line as:
y - 1 = 2(x - 0.5)
Simplifying, we get:
y = 2x - 0.5
Substituting x = 0.5 and y = -1, we get:
-1 ≠ 2(0.5) - 0.5
So, this is not a solution and we can eliminate this option.
Therefore, none of the given systems of equations show a solution of (0.5, -1).
Option A: On a coordinate plane, 2 lines intersect at (0.5, negative 1).
We don't have any equations to work with, so we cannot check this option.
Option B: On a coordinate plane, 2 lines intersect at (negative 0.5, negative 1).
Again, we don't have any equations to work with, so we cannot check this option.
Option C: On a coordinate plane, 2 lines intersect at (negative 0.5, 1).
The x-coordinate is not 0.5, so this is not a solution. Eliminate this option.
Option D: On a coordinate plane, 2 lines intersect at (0.5, 1).
Let's write the equations of the two lines passing through (0.5, 1) and (-0.5, -1) respectively and then substitute (0.5, -1) in them:
Line 1: Passing through (0.5, 1) with slope (1 - (-1))/(0.5 - (-0.5)) = 2/1 = 2, we can write the point-slope form of the line as:
y - 1 = 2(x - 0.5)
Simplifying, we get:
y = 2x - 0.5
Substituting x = 0.5 and y = -1, we get:
-1 ≠ 2(0.5) - 0.5
So, this is not a solution and we can eliminate this option.
Therefore, none of the given systems of equations show a solution of (0.5, -1).
look again
1 answer