Solve the following system of linear equations

Question

1. 3x − y = 0

−x + y = 4

2. x + 2y = 5

x + 5y = 9

3. 3x − y = −2

−5x + y = −10

4. x + y = 0

4x − y = −3

Answer 1

1.

3x − y = 0

Multiply the second equation by 3

3(−x + y) = 3(4) -> -3x + 3y = 12

Adding the two equations together

3x - y + -3x + 3y = 0 + 12

Combining like terms

2y = 12

y = 6

Plugging y = 6 back in to the first equation

3x - 6 = 0

3x = 6

x = 2

(x,y) = (2,6)

The process is similar for the other 4 problems so I hope this gets you started!