Solve the system x + y = 5 and 2x - y = 4.
Solution
Problem
Solve the system x + y = 5 and 2x - y = 4.
Step 1: Write the system.
x + y = 5
2x - y = 4
Step 2: Add the equations.
Adding the left sides and right sides gives:
(x + y) + (2x - y) = 5 + 4
The y terms cancel:
3x = 9
Step 3: Solve for x.
Divide both sides by 3:
x = 3
Step 4: Substitute x = 3 into one of the original equations.
Use x + y = 5:
3 + y = 5
Step 5: Solve for y.
y = 2
Step 6: Check the solution in the second equation.
2(3) - 2 = 6 - 2 = 4
The equation is satisfied.
Therefore, the solution is (3, 2).
Result
x = 3, y = 2