Ximpledu

System of Linear Equations

See how to solve a system of linear equations
and graph a system of linear inequalities.
16 examples and their solutions.

System of Linear Equations: Using Graph

Example

x - y = 4
2x + y = 5
Solution

Example

x - y = 4
2x - 2y = 8
Solution

Example

x - y = 4
x - y = -3
Solution

Substitution Method

Example

x - y = 4
2x + y = 5
Solution

Example

x - y = 4
2x - 2y = 8
Solution

Example

x - y = 4
x - y = -3
Solution

Elimination Method

Example

x - y = 4
2x + y = 5
Solution

Example

3x + 2y = 7
2x - 3y = -4
Solution

Example

x - y = 4
2x - 2y = 8
Solution

Example

x - y = 4
x - y = -3
Solution

System of Linear Inequalities

Example

x + y > 2
2x - y ≥ 3
Solution

Example

2x - y > -3
2x - y ≥ 1
Solution

Example

3x + y ≥ 4
3x + y < -2
Solution

Linear Programming

Example

For the given system of linear inequalities,
find the maximum value of x + y.

x ≥ 0
y ≥ 0
3x + y ≤ 9
x + 2y ≤ 8
Solution

System of Equations (Three Variables)

Example

x + y + z = 3
2x - y + z = 6
x + 2y - z = -4
Solution

Example

x + 4y = 5
y + 4z = 7
z + 4x = 8
x + y + z = ?
Solution