To solve this system of linear equations by first graphing, we will graph the two lines representing each equation y=4x-5 and y=-x+5 on the same coordinate plane and find the point of intersection which is our solution.
Let's start with the equation y=4x-5:
This is a linear equation with a slope of 4 and y-intercept of -5. Plot the y-intercept at point (0, -5) and use the slope to find another point on the line.
Slope of 4 means for every 1 unit moved right, we move 4 units up. Connect the two points to draw the line y=4x-5.
Next, let's graph the equation y=-x+5:
This is another linear equation with a slope of -1 and y-intercept of 5. Plot the y-intercept at point (0, 5) and use the slope to find another point on the line.
Slope of -1 means for every 1 unit moved right, we move 1 unit down. Connect the two points to draw the line y=-x+5.
Now on your graph, mark the point of intersection of the two lines, this is the solution to the system of equations y=4x-5 and y=-x+5.
The point of intersection appears to be at (2, 3). Therefore, the solution to the system of equations is x = 2 and y = 3.
solve the following system of linear equtions by first graphing the system y=4x-5 y=-x+5
3 answers
wrong
I apologize for the mistake in my previous response. Let's correct that and find the correct solution to the system of equations y=4x-5 and y=-x+5 by graphing:
To graph the first equation y=4x-5:
Plot the y-intercept at (0, -5) and use the slope of 4 to find another point.
For every unit moved to the right, move 4 units up.
To graph the second equation y=-x+5:
Plot the y-intercept at (0, 5) and use the slope of -1 to find another point.
For every unit moved to the right, move 1 unit down.
Now, with both equations graphed on the same coordinate axes, we can visually see where the two lines intersect. This intersection point represents the solution to the system of equations.
Upon graphing, it should be clear that the two lines intersect at the point (2, 3). This means that the correct solution to the system of equations y=4x-5 and y=-x+5 is x = 2 and y = 3.
To graph the first equation y=4x-5:
Plot the y-intercept at (0, -5) and use the slope of 4 to find another point.
For every unit moved to the right, move 4 units up.
To graph the second equation y=-x+5:
Plot the y-intercept at (0, 5) and use the slope of -1 to find another point.
For every unit moved to the right, move 1 unit down.
Now, with both equations graphed on the same coordinate axes, we can visually see where the two lines intersect. This intersection point represents the solution to the system of equations.
Upon graphing, it should be clear that the two lines intersect at the point (2, 3). This means that the correct solution to the system of equations y=4x-5 and y=-x+5 is x = 2 and y = 3.