Answer:
Explanation:
To solve the system of linear equations using the addition/elimination method, you can manipulate the equations to eliminate one of the variables. Here's how you can do it:
Start with the original equations:
4x + 2y = 2 ...(1)
3x - y = -1 ...(2)
To eliminate "y," multiply equation (2) by 2 so that the coefficients of "y" in both equations become equal:
2(3x - y) = 2(-1)
This simplifies to:
6x - 2y = -2 ...(3)
Now, you have the modified equation (3) and the original equation (1). You can add these two equations together to eliminate "y":
(4x + 2y) + (6x - 2y) = 2 + (-2)
Combine like terms:
4x + 6x = 0
10x = 0
Divide by 10 to solve for "x":
x = 0
Now that you have the value of "x," you can substitute it into equation (2) to solve for "y":
3x - y = -1
3(0) - y = -1
0 - y = -1
-y = -1
To isolate "y," multiply both sides by -1:
y = 1
So, the solution to the system of equations is:
x = 0
y = 1
Now, you can graphically represent this solution by plotting the point (0, 1) on a coordinate plane. This is the point where the two lines representing the equations intersect.
Here's how the equations look when graphed:
Equation (1): 4x + 2y = 2
Equation (2): 3x - y = -1
The point of intersection is (0, 1).