3x + y = 3
x + y = 2
Solve the system of equations.
Responses
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
1. Solve one of the equations for one variable in terms of the other. Let's solve the second equation for x:
x + y = 2
x = 2 - y
2. Substitute the expression for x into the other equation:
3(2 - y) + y = 3
3. Simplify the equation:
6 - 3y + y = 3
6 - 2y = 3
4. Solve for y:
-2y = 3 - 6
-2y = -3
y = -3 / -2
y = 3/2
5. Substitute the value of y back into the equation for x:
x + y = 2
x + 3/2 = 2
x = 2 - 3/2
x = 4/2 - 3/2
x = 1/2
Therefore, the solution to the system of equations is x = 1/2 and y = 3/2.