The system of equations is:
y = -2x + 3
-2x = y +1
This can be rewritten as:
y = -2x + 3
y = -2x -1
Here's how to graph this system of equations:
1. Plot the line y = -2x + 3.
• The y-intercept is 3, meaning the line crosses the y-axis at the point (0,3). Plot this point on the graph.
• The slope is -2, meaning it goes down 2 units on the y-axis for every 1 unit it goes along the x-axis.
2. Plot the line y = -2x - 1
• The y-intercept is -1, meaning the line crosses the y-axis at the point (0,-1). Plot this point on the graph.
• The slope is -2, the same as before, so trace out the same pattern on the graph.
When you graph these two lines, you will see that they are parallel so they never intersect. Hence there are no solutions to the system. This means these two equations are inconsistent. It would mean one variable equals two different numbers which isn't possible.
So the solution is the empty set or ∅.
Solve the system of equations by graphing.
y=-2x + 3
-2x = y +1
5 answers
are you sure
I apologize, there was a mistake in the first analysis. Let's correct that.
The system of equations is:
1) y = -2x + 3
2) -2x = y +1
The second equation can be rewritten as:
y = -2x - 1
So the correct system of equations is:
1) y = -2x + 3
2) y = -2x - 1
The general form of the line equation is y = mx + b, where m is the slope, and b is the y-intercept. Here, both lines have the same slope (-2), but different y-intercepts (3 and -1), so the lines are parallel and do not intersect.
This means the system of equations has no solution. The previous conclusion was correct. I apologize for any confusion.
The system of equations is:
1) y = -2x + 3
2) -2x = y +1
The second equation can be rewritten as:
y = -2x - 1
So the correct system of equations is:
1) y = -2x + 3
2) y = -2x - 1
The general form of the line equation is y = mx + b, where m is the slope, and b is the y-intercept. Here, both lines have the same slope (-2), but different y-intercepts (3 and -1), so the lines are parallel and do not intersect.
This means the system of equations has no solution. The previous conclusion was correct. I apologize for any confusion.
Solve the system of equations by graphing.
X = 4
Y = 2x - 3
X = 4
Y = 2x - 3
To solve this system of equations by graphing, you'd plot both equations on the same set of axes and look for their point of intersection which represents the solution to the system.
The first equation is X = 4, which is a vertical line that passes through the x-axis at x = 4.
The second equation is Y = 2x - 3, which is a straight line with a slope of 2 and a y-intercept of -3.
When you graph these two lines, you'll find that they intersect at the point (4,-1) Therefore, the solution to the system is x = 4 and y = -1.
The first equation is X = 4, which is a vertical line that passes through the x-axis at x = 4.
The second equation is Y = 2x - 3, which is a straight line with a slope of 2 and a y-intercept of -3.
When you graph these two lines, you'll find that they intersect at the point (4,-1) Therefore, the solution to the system is x = 4 and y = -1.
1 answer