How many solutions does this linear system have? y = 2x - 5 and -8x - 4y = -20

Solution:

It is given that

y = 2x - 5

2x - y = 5 …. (1)

-8x - 4y = -20

Divide both sides by -4

2x + y = 5 …. (2)

From both the linear equations we know that

a₁ = 2

b₁ = -1

c₁ = 5

a₂ = 2

b₂ = 1

c₂ = 5

Here a₂/a₁ = b₂/b₁

Substituting the values

2/2 = 1/-1

1 ≠ -1

Thus on solving the system of linear equations, we get an intersecting line that has a unique solution and it is (5/2,0)

Therefore, the linear system has only one solution.

How many solutions does this linear system have? y = 2x - 5 and -8x - 4y = -20

Summary:

The linear system y = 2x - 5 and -8x - 4y = -20 has only one solution.