Solve the system by graphing. Check your solution.
4x - y = 8
-2x - y = 2
To graph the system, we need to create a linear equation in slope-intercept form (y = mx + b) for each equation.
For the first equation, 4x - y = 8, we can rearrange it to solve for y:
y = 4x - 8
For the second equation, -2x - y = 2, we can rearrange it to solve for y:
y = -2x - 2
Now that we have the equations in slope-intercept form, we can graph them:
First equation: y = 4x - 8
To graph this equation, we can start by plotting the y-intercept, which is -8. Then, we can use the slope (4) to find additional points. Since the slope is positive, we can go up 4 units and to the right 1 unit to find another point. Finally, we can draw a straight line through these two points.
Second equation: y = -2x - 2
To graph this equation, we can start by plotting the y-intercept, which is -2. Then, we can use the slope (-2) to find additional points. Since the slope is negative, we can go down 2 units and to the right 1 unit to find another point. Finally, we can draw a straight line through these two points.
After graphing the two equations, we can see that they intersect at the point (2, -0).
To check the solution, we can substitute the x and y coordinates of the point of intersection (2, -0) into the original system of equations:
For the first equation: 4(2) - (-0) = 8
The left side simplifies to 8 + 0 = 8, which is true.
For the second equation: -2(2) - (-0) = 2
The left side simplifies to -4 + 0 = 2, which is false.
Since one of the equations is not true for the point of intersection, the solution is not valid. Thus, there is no solution to the system.