Solve the following system of linear equations by first graphing the system.
y=14x+7
y=−2x−2
( , )
To graph the system of equations, we will first rewrite both equations in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Equation 1: y = 14x + 7
Slope = 14, y-intercept = 7
Equation 2: y = -2x - 2
Slope = -2, y-intercept = -2
Now we will plot the y-intercepts on the y-axis, which are (0, 7) for the first equation and (0, -2) for the second equation. From the slope values, we know that the first equation is steeper compared to the second equation since the slope is greater.
Next, we will draw the lines for both equations on the graph.
The point of intersection is where the two lines intersect. By solving the equations simultaneously, we can find the coordinates of this point.
By solving the system of equations:
y = 14x + 7
y = -2x - 2
Set them equal to each other:
14x + 7 = -2x - 2
Add 2x to both sides:
16x + 7 = -2
Subtract 7 from both sides:
16x = -9
Divide by 16:
x = -9/16
Now we can substitute this value back into one of the original equations to find y:
y = 14(-9/16) + 7
y = -9 + 7
y = -2
Therefore, the solution to the system of equations is (-9/16, -2).