Question
Solve the system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.
y = x + 1
y = x - 1
y = x + 1
y = x - 1
Answers
Answer
Solve the system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.
y = x - 3
y = x + 3
y = x - 3
y = x + 3
Answered by
GPT 3.5
To solve the system by graphing, we will graph each equation on the same coordinate plane and find where they intersect.
The first equation, y = x + 1, is a linear equation in slope-intercept form (y = mx + b), where the slope (m) is 1 and the y-intercept (b) is 1. We can start by plotting the y-intercept at (0, 1), and then find another point by using the slope. From the y-intercept, we move 1 unit up (y-axis) and 1 unit to the right (x-axis). This gives us the point (1, 2). We can now draw a line passing through these two points.
The second equation, y = x - 1, is also a linear equation in slope-intercept form with a slope of 1 and a y-intercept of -1. We can plot the y-intercept at (0, -1) and find another point using the slope. From the y-intercept, we move 1 unit up and 1 unit to the right to get the point (1, 0). We can now draw a line passing through these two points.
Graphing both lines on the same coordinate plane, we get two lines that are parallel and never intersect. Therefore, the system has no solution.
The first equation, y = x + 1, is a linear equation in slope-intercept form (y = mx + b), where the slope (m) is 1 and the y-intercept (b) is 1. We can start by plotting the y-intercept at (0, 1), and then find another point by using the slope. From the y-intercept, we move 1 unit up (y-axis) and 1 unit to the right (x-axis). This gives us the point (1, 2). We can now draw a line passing through these two points.
The second equation, y = x - 1, is also a linear equation in slope-intercept form with a slope of 1 and a y-intercept of -1. We can plot the y-intercept at (0, -1) and find another point using the slope. From the y-intercept, we move 1 unit up and 1 unit to the right to get the point (1, 0). We can now draw a line passing through these two points.
Graphing both lines on the same coordinate plane, we get two lines that are parallel and never intersect. Therefore, the system has no solution.
Answered by
GPT 3.5
To solve the system by graphing, we will graph each equation on the same coordinate plane and find where they intersect.
The first equation, y = x - 3, is a linear equation in slope-intercept form (y = mx + b), where the slope (m) is 1 and the y-intercept (b) is -3. We can start by plotting the y-intercept at (0, -3), and then find another point by using the slope. From the y-intercept, we move 1 unit up (y-axis) and 1 unit to the right (x-axis). This gives us the point (1, -2). We can now draw a line passing through these two points.
The second equation, y = x + 3, is also a linear equation in slope-intercept form with a slope of 1 and a y-intercept of 3. We can plot the y-intercept at (0, 3) and find another point using the slope. From the y-intercept, we move 1 unit up and 1 unit to the right to get the point (1, 4). We can now draw a line passing through these two points.
Graphing both lines on the same coordinate plane, we get two lines that are parallel and never intersect. Therefore, the system has no solution.
The first equation, y = x - 3, is a linear equation in slope-intercept form (y = mx + b), where the slope (m) is 1 and the y-intercept (b) is -3. We can start by plotting the y-intercept at (0, -3), and then find another point by using the slope. From the y-intercept, we move 1 unit up (y-axis) and 1 unit to the right (x-axis). This gives us the point (1, -2). We can now draw a line passing through these two points.
The second equation, y = x + 3, is also a linear equation in slope-intercept form with a slope of 1 and a y-intercept of 3. We can plot the y-intercept at (0, 3) and find another point using the slope. From the y-intercept, we move 1 unit up and 1 unit to the right to get the point (1, 4). We can now draw a line passing through these two points.
Graphing both lines on the same coordinate plane, we get two lines that are parallel and never intersect. Therefore, the system has no solution.
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