Question
how many solutions does -2x + y = 6 have
Answers
Answer
solve the given systems of linear equations by inspection
y = 3/5x - 5
and
y = -
3/5x - 5
y = 3/5x - 5
and
y = -
3/5x - 5
Answer
how do you find the solution to a systems of equations graphically?
Answer
how do you find the solution to a systems of equations graphically?
A,Find the point where the two lines intersect
B.find the y-intercept of the two lines
C.find the slope of the two lines
D.find the slope and y-intercept of the two lines
A,Find the point where the two lines intersect
B.find the y-intercept of the two lines
C.find the slope of the two lines
D.find the slope and y-intercept of the two lines
Answer
what will the graph look like for a systems of equations that has no solution?
A. you will see the lines intersect at two different points
B.you will see the lines on top of each other so that they form the same exact line
C. you will see the lines intersect at only one point
D.you will see parallel lines
E. you will see perpendicular lines
A. you will see the lines intersect at two different points
B.you will see the lines on top of each other so that they form the same exact line
C. you will see the lines intersect at only one point
D.you will see parallel lines
E. you will see perpendicular lines
Answer
how do you find the solution to a systems of equations graphically?
Answered by
GPT 3.5
The equation -2x + y = 6 represents a linear equation that can be graphed as a straight line. The number of solutions for this equation depends on the slope of the line. In this case, the slope of the line is -2.
If the slope is nonzero, the equation will have exactly one solution.
If the slope is zero, the equation will either have infinitely many solutions or no solution.
Since the slope of the line -2x + y = 6 is not zero, it will have exactly one solution.
If the slope is nonzero, the equation will have exactly one solution.
If the slope is zero, the equation will either have infinitely many solutions or no solution.
Since the slope of the line -2x + y = 6 is not zero, it will have exactly one solution.
Answered by
GPT 3.5
To solve the system of linear equations by inspection, we can set the two equations equal to each other and solve for x.
So, we have:
3/5x - 5 = -3/5x - 5
Let's add 3/5x to both sides to eliminate it from the right side of the equation:
3/5x + 3/5x - 5 = - 5
Combining like terms on the left side:
(3/5x + 3/5x) - 5 = -5
6/5x - 5 = -5
Now, let's add 5 to both sides to eliminate it from the left side of the equation:
6/5x - 5 + 5 = -5 + 5
6/5x = 0
To solve for x, we can multiply both sides by 5/6:
(6/5x)(5/6) = 0(5/6)
x = 0
Now that we know x = 0, we can substitute this value into either of the original equations to solve for y. Let's use the first equation y = 3/5x - 5:
y = 3/5(0) - 5
y = 0 - 5
y = -5
Therefore, the solution to the system of linear equations is x = 0 and y = -5.
So, we have:
3/5x - 5 = -3/5x - 5
Let's add 3/5x to both sides to eliminate it from the right side of the equation:
3/5x + 3/5x - 5 = - 5
Combining like terms on the left side:
(3/5x + 3/5x) - 5 = -5
6/5x - 5 = -5
Now, let's add 5 to both sides to eliminate it from the left side of the equation:
6/5x - 5 + 5 = -5 + 5
6/5x = 0
To solve for x, we can multiply both sides by 5/6:
(6/5x)(5/6) = 0(5/6)
x = 0
Now that we know x = 0, we can substitute this value into either of the original equations to solve for y. Let's use the first equation y = 3/5x - 5:
y = 3/5(0) - 5
y = 0 - 5
y = -5
Therefore, the solution to the system of linear equations is x = 0 and y = -5.
Answered by
GPT 3.5
To find the solution to a system of equations graphically, you will plot the graphs of the equations on the same coordinate system and determine the point of intersection. The point of intersection represents the solution to the system of equations.
Here are the steps to find the solution graphically:
1. Write the given equations in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
2. Plot the y-intercept for each equation on the y-axis.
3. Use the slope of each equation to identify additional points on the graph. For example, if the slope is 2/3, it means that for every 3 units moved horizontally, you move 2 units vertically.
4. Once you have at least two points on each graph, plot them and draw a straight line through the points.
5. Repeat steps 2-4 for the second equation.
6. Look for the point where the two lines intersect. This is the solution to the system of equations.
7. If the lines are parallel and do not intersect at any point, it means there is no solution to the system of equations.
8. If the two lines are the same, or coincident, it means there are infinitely many solutions to the system of equations.
By following these steps and interpreting the graphical representation of the equations, you can find the solution to a system of equations.
Here are the steps to find the solution graphically:
1. Write the given equations in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
2. Plot the y-intercept for each equation on the y-axis.
3. Use the slope of each equation to identify additional points on the graph. For example, if the slope is 2/3, it means that for every 3 units moved horizontally, you move 2 units vertically.
4. Once you have at least two points on each graph, plot them and draw a straight line through the points.
5. Repeat steps 2-4 for the second equation.
6. Look for the point where the two lines intersect. This is the solution to the system of equations.
7. If the lines are parallel and do not intersect at any point, it means there is no solution to the system of equations.
8. If the two lines are the same, or coincident, it means there are infinitely many solutions to the system of equations.
By following these steps and interpreting the graphical representation of the equations, you can find the solution to a system of equations.
Answered by
GPT 3.5
To find the solution to a system of equations graphically, you can follow these steps:
1. Write the given equations in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
2. Graph each equation on the same coordinate plane.
3. Determine the point where the two lines intersect.
4. Reading the coordinates of the point of intersection will give you the solution to the system of equations.
Option A (Find the point where the two lines intersect) is the correct answer. This is where the x-value and y-value are the same for both equations, representing the solution to the system of equations.
Option B (Find the y-intercept of the two lines) refers to the value of y when x is equal to zero. The y-intercept represents the point where the line crosses the y-axis.
Option C (Find the slope of the two lines) refers to the steepness or incline of a line. It determines how much the y-value changes for a given change in x-value.
Option D (Find the slope and y-intercept of the two lines) combines finding the slope and the y-intercept of each line individually. The slope determines the line's steepness, and the y-intercept represents the point where the line crosses the y-axis.
Overall, by graphing the equations and inspecting where the lines intersect, you can determine the solution to a system of equations graphically.
1. Write the given equations in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
2. Graph each equation on the same coordinate plane.
3. Determine the point where the two lines intersect.
4. Reading the coordinates of the point of intersection will give you the solution to the system of equations.
Option A (Find the point where the two lines intersect) is the correct answer. This is where the x-value and y-value are the same for both equations, representing the solution to the system of equations.
Option B (Find the y-intercept of the two lines) refers to the value of y when x is equal to zero. The y-intercept represents the point where the line crosses the y-axis.
Option C (Find the slope of the two lines) refers to the steepness or incline of a line. It determines how much the y-value changes for a given change in x-value.
Option D (Find the slope and y-intercept of the two lines) combines finding the slope and the y-intercept of each line individually. The slope determines the line's steepness, and the y-intercept represents the point where the line crosses the y-axis.
Overall, by graphing the equations and inspecting where the lines intersect, you can determine the solution to a system of equations graphically.
Answered by
GPT 3.5
The correct answer is D. You will see parallel lines.
When a system of equations has no solution, it means that the lines represented by the equations are parallel and will never intersect. Graphically, this means that the lines will run parallel to each other and never cross paths.
When a system of equations has no solution, it means that the lines represented by the equations are parallel and will never intersect. Graphically, this means that the lines will run parallel to each other and never cross paths.
Answered by
GPT 3.5
To find the solution to a system of equations graphically, you can follow these steps:
1. Write the given equations in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
2. Graph each equation on the same coordinate plane.
3. Locate the point where the two lines intersect.
4. Read the coordinates of the point of intersection.
5. The coordinates of the point of intersection represent the solution to the system of equations.
- The x-coordinate is the value of x that satisfies both equations simultaneously.
- The y-coordinate is the value of y that satisfies both equations simultaneously.
By graphing the equations and identifying the point where they intersect, you can visually determine the solution to the system of equations.
1. Write the given equations in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
2. Graph each equation on the same coordinate plane.
3. Locate the point where the two lines intersect.
4. Read the coordinates of the point of intersection.
5. The coordinates of the point of intersection represent the solution to the system of equations.
- The x-coordinate is the value of x that satisfies both equations simultaneously.
- The y-coordinate is the value of y that satisfies both equations simultaneously.
By graphing the equations and identifying the point where they intersect, you can visually determine the solution to the system of equations.
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