# 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

a_{1} = 2

b_{1} = -1

c_{1} = 5

a_{2} = 2

b_{2} = 1

c_{2} = 5

Here a_{2}/a_{1} = b_{2}/b_{1}

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.

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