solve each system of equations by graphing
y=x+1
y=3x-7
this is an easy one to graph.
just pick some values for x or y and solve for the other value
what are you having trouble doing?
we can't graph it for you.
for y = x + 1
x = 0, y = 1 (0,1)
x = 1, y = 2 (1,2)
x = 2, y = 3 (2,3)
x = 3, y = 4 (3.4)
x = 4, y = 5 (4,5)
for
y = 3x - 7
for x = 0, y = -7 (0,-7)
for x = 1, y = -4 (1,-4)
for x = 2, y = -1 (2,-1)
for x = 3, y = 2 (3,2)
for x = 4, y = 5 (4,5)
plot points for each and solve
To solve a system of equations by graphing, you need to plot the graphs of each equation on the same coordinate plane and find the point of intersection. The point of intersection represents the solution to the system of equations.
Let's solve the system of equations:
1) y = x + 1
2) y = 3x - 7
Step 1: Choose an appropriate scale for the x and y axes. For simplicity, assume a scale of 1 unit for each grid line.
Step 2: For the first equation, y = x + 1, identify two points on the graph. You can do this by picking any values for x and finding the corresponding y values. For example, when x = 0, y = 0 + 1 = 1. So we have the point (0, 1). Similarly, when x = -2, y = -2 + 1 = -1. So we have the point (-2, -1).
Step 3: Plot these points on the coordinate plane and draw a straight line through them. This line represents the graph of the equation y = x + 1.
Step 4: Repeat steps 2 and 3 for the second equation, y = 3x - 7. When x = 0, y = 3(0) - 7 = -7. So we have the point (0, -7). When x = -2, y = 3(-2) - 7 = -13. So we have the point (-2, -13).
Step 5: Plot these points on the coordinate plane and draw a straight line through them. This line represents the graph of the equation y = 3x - 7.
Step 6: Now, analyze the graph and find the point where the two lines intersect. This point represents the solution to the system of equations.
In this case, it should be clear that the lines intersect at the point (2, 3). Therefore, the solution to the system of equations y = x + 1 and y = 3x - 7 is x = 2 and y = 3.
Please note that graphing is just one method to solve a system of equations. There are other methods like substitution and elimination that may be more efficient for certain cases.