Solve the following system of linear equations by first graphing the system.
y=14x+7
y=−2x−2
(1 point)
(
,
)
To graph the system, we will first plot the two equations on the same graph.
For the equation y = 14x + 7:
- Plot the y-intercept at (0,7)
- Use the slope of 14 to find another point, such as going up 14 units and over 1 unit from the y-intercept.
For the equation y = -2x - 2:
- Plot the y-intercept at (0,-2)
- Use the slope of -2 to find another point, such as going down 2 units and over 1 unit from the y-intercept.
Now, plot both lines on the same graph and find the point of intersection. The solution to the system of equations is the coordinates of the point of intersection.
After graphing, the point of intersection is approximately (0.5, 7). Therefore, the solution to the system of equations is:
(0.5, 7)
what?? where did you get the decimal?
I apologize for the mistake. Let's find the solution without decimals.
To solve the system of equations y = 14x + 7 and y = -2x - 2, we can set the two equations equal to each other:
14x + 7 = -2x - 2
Combine like terms:
16x + 7 = -2
Subtract 7 from both sides:
16x = -9
Divide by 16:
x = -9/16
Now, substitute the value of x back into one of the equations to find the value of y:
y = 14(-9/16) + 7
y = -126/16 + 7
y = -63/8 + 56/8
y = -7/8
Therefore, the solution to the system of equations is:
x = -9/16
y = -7/8