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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

Verified Answer :

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:

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

Step-by-step 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.