Solve the system

Question

4x₁+x₂=-3

8x₁+2x₂=-6

 

x1=

x2=

 

Answer 1

If you multiply the first equation by 2 you get the second equation.

Because the equations are identical, the system is dependent and has infinitely many solutions

Answer 2

Attempting to solve this with the substitution method, we have

x₂ = 3 - 4x₁

Substituting this into the second equation, we end up with

0 = 0.

 

There are infinitely many solutions for these two equations.

The solution set consists of all points on the line 4x₁+ x₂ = 3

for example,

x₁ = 1,  x₂ = -1

x₁ = 0,  x₂ = 3