use linear combinations to solve the system of linear equations.

2x+y=4
x-y=2

2x+y=4

2x-2y=4
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3 y = 0
y = 0
x = 2

To solve the system of linear equations using linear combinations, also known as the method of elimination, follow the steps below:

Step 1: Choose one of the variables to eliminate by multiplying one or both equations by suitable constants so that the coefficients of the chosen variable will be the same or differ only by their signs. In this case, let's eliminate the variable "y".

Step 2: Multiply the second equation by 2 to make the coefficients of "y" in both equations the same.

(2x + y = 4) × 2
(x - y = 2) × 2

Simplifying the equations, we get:
4x + 2y = 8 (equation 1)
2x - 2y = 4 (equation 2)

Step 3: Add the modified equations to eliminate the variable "y". In this case, we add equation 1 and equation 2:

(4x + 2y) + (2x - 2y) = 8 + 4

Simplifying the equation, we get:
6x = 12

Step 4: Solve for x by dividing both sides of the equation by 6:

6x/6 = 12/6
x = 2

Step 5: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:

2(2) + y = 4

Simplifying the equation, we have:
4 + y = 4

Step 6: Solve for y by subtracting 4 from both sides of the equation:

4 + y - 4 = 4 - 4
y = 0

So the solution to the system of linear equations is x = 2 and y = 0.