Solve each system by graphing. Check your solution.
11) y=1/2 x + 7 y=3/2 x + 7
13) y=x - 4 y= - x
Can someone help me understand help me figure it out these two question??
the solution is the intersection of the two lines
graph the lines and see where they cross
there are graphing utilities online
... fooplot is one
Of course! I'd be happy to help you understand how to solve these systems of equations by graphing.
To solve the first system of equations, which is:
11) y = (1/2)x + 7
y = (3/2)x + 7
Step 1: Start by graphing each equation on the same coordinate plane. To do this, choose some x-values and find the corresponding y-values for each equation. For example, you could choose x = 0, x = 1, and x = -1, and find the y-values for each equation.
For the first equation y = (1/2)x + 7:
When x = 0, y = (1/2)(0) + 7 = 7
When x = 1, y = (1/2)(1) + 7 = 7.5
When x = -1, y = (1/2)(-1) + 7 = 6.5
For the second equation y = (3/2)x + 7:
When x = 0, y = (3/2)(0) + 7 = 7
When x = 1, y = (3/2)(1) + 7 = 8.5
When x = -1, y = (3/2)(-1) + 7 = 6.5
Plot the points (0, 7), (1, 7.5), (-1, 6.5) for the first equation, and plot the points (0, 7), (1, 8.5), (-1, 6.5) for the second equation.
Step 2: Once you have plotted the points for each equation, draw a straight line through the points for each equation.
Step 3: Check the intersection point of the two lines. The coordinates of this intersection point represent the solution to the system of equations.
Now, let's move on to solving the second system of equations:
13) y = x - 4
y = -x
Step 1: Again, we start by graphing each equation on the same coordinate plane. Choose some x-values and find the corresponding y-values for each equation. For example, you could choose x = 0, x = 1, and x = -1, and find the y-values for each equation.
For the first equation y = x - 4:
When x = 0, y = 0 - 4 = -4
When x = 1, y = 1 - 4 = -3
When x = -1, y = -1 - 4 = -5
For the second equation y = -x:
When x = 0, y = -(0) = 0
When x = 1, y = -(1) = -1
When x = -1, y = -(-1) = 1
Plot the points (0, -4), (1, -3), (-1, -5) for the first equation, and plot the points (0, 0), (1, -1), (-1, 1) for the second equation.
Step 2: Draw a straight line through the points for each equation.
Step 3: Check the intersection point of the two lines. The coordinates of this intersection point represent the solution to the system of equations.
I hope this helps you understand how to solve these systems of equations by graphing! Let me know if you have any further questions.