Simultaneous equations are two equations with two unknowns that must be solved together to find unique values for both variables.
2x + y = 7
x - y = 2
Find values of x and y that satisfy both equations
Add or subtract equations to eliminate one variable, then solve for the other.
Step 1: Add the equations (to eliminate y)
(2x + y) + (x - y) = 7 + 2
3x = 9
x = 3
Step 2: Substitute x = 3 into first equation
2(3) + y = 7
6 + y = 7
y = 1
Solution: x = 3, y = 1
Solve one equation for one variable, then substitute into the other equation.
Step 1: From first equation: x = 8 - 2y
Step 2: Substitute into second equation
3(8 - 2y) - y = 5
24 - 6y - y = 5
24 - 7y = 5
-7y = -19
y = 19/7
Step 3: Find x: x = 8 - 2(19/7) = 18/7
1. Solve using elimination: x + y = 5 and x - y = 1