x + y = 4

2x - 3y = -2

using the substitution method

To solve this system of linear equations, we can use the method of substitution. Here's how you can solve it step by step:

Step 1: Solve one equation for one variable in terms of the other variable.
In the first equation, solve for x: x = 4 - y.

Step 2: Substitute the expression found in step 1 into the other equation.
Replace x in the second equation with the expression (4 - y):
2(4 - y) - 3y = -2.

Step 3: Simplify and solve the resulting equation for y.
Expand and simplify the equation:
8 - 2y - 3y = -2.
Combine like terms:
-5y + 8 = -2.
Subtract 8 from both sides:
-5y = -10.
Divide both sides by -5:
y = 2.

Step 4: Substitute the value found in step 3 into one of the original equations to solve for the other variable.
Using the first equation: x + 2 = 4.
Subtract 2 from both sides:
x = 2.

Step 5: Check the solution by substituting the values of x and y into the other equation.
Using the second equation:
2(2) - 3(2) = -2.
4 - 6 = -2.
-2 = -2.

Therefore, the solution to the system of equations is x = 2 and y = 2.