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.
Solve the system by graphing. Check your solution.
4x - y = 8
-2x - y = 2
1 answer