Question

Y = 5x – 1

–15x – 3y = 3
How many solutions does this linear system have?

one solution: (0, –1)
one solution: (1, 4)
no solution
infinite number of solutions

Answer 1

y=5x-1
-15x-3y=3
-15x-15x+3=3
-30x=0
x=0
therefore y=5x0 -1= -1
so one solution(0,-1)

Answer 2

Option 1 - There is one solution : (0,-1)

Explanation:

Given : The system of equations
`y=5x-1` and
`-15x-3y=3`

To find : How many solutions does this linear system have?

Solution :

Let Equation (1),
`y=5x-1`

Equation (2),
`-15x-3y=3`

Applying substitution method,

Substitute y from equation (1) into (2),

`-15x-3y=3`

`-15x-3(5x-1)=3`

`-15x-15x+3=3`

`-30x=0`

`x=0`

Substitute in equation (1),

`y=5x-1`

`y=5(0)-1`

`y=-1`

Therefore, There is one solution : (0,-1)

So, Option 1 is correct.