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

one solution: (0, –1)

Explanation:

we have

`y=5x-1` ----> equation A

`-15x-3y=3` ----> equation B

isolate the variable y in the equation B

`3y=-15x-3`

`y=-5x-1` ----> equation C

Compare equation A and equation C

The equations are different

The slopes are different ( are not parallel lines)

therefore

The system has one solution

Solve the system

equate the equation A and equation C and solve for x

`5x-1=-5x-1`

`5x+5x=-1+1`

`x=0`

Find the value of y

`y=5(0)-1=-1`

The solution is the point (0,-1)