Solve the following system of linear equations by first graphing the system. y=14x+7 y=−2x−2
To graph the system of linear equations, we will find the points of intersection between the two lines represented by each equation.
For the first equation y = 14x + 7:
We can start by finding two points on this line:
When x = 0, y = 7. So, one point on the line is (0, 7).
When x = 1, y = 14*1 + 7 = 21. So, another point on the line is (1, 21).
For the second equation y = -2x - 2:
When x = 0, y = -2*0 - 2 = -2. So, one point on the line is (0, -2).
When x = 1, y = -2*1 - 2 = -4. So, another point on the line is (1, -4).
Now we can plot these points on a graph and draw the lines:
For y = 14x + 7, the line passes through the points (0, 7) and (1, 21).
For y = -2x - 2, the line passes through the points (0, -2) and (1, -4).
Now, we can see that the two lines intersect at the point (1, 21), which is the solution to the system of equations.
Therefore, the solution to the system of equations is x = 1, y = 21.