Question

$y=5x-1;-15x-3y=3$

How many solution does this linear system have?

• A. one solution: $\left(0,-1\right)$
• B. one solution: $\left(1,4\right)$
• C. no solution
• D. infinite number of solutions

Answer 1

The correct option is A

one solution: $\left(0,-1\right)$

Explanation for the correct option:

Option$\left(A\right)$:

The given system of equation is

$$\begin{gathered} y=5x-1.....\left(1\right) \\ -15x-3y=3.....\left(2\right) \end{gathered}$$

$\Rightarrow -15x-3(5x-1)=3$ [Substituting $y$]

$$\begin{gathered} \Rightarrow -15x-3(5x-1)=3 \\ \Rightarrow -15x-15x+3=3 \\ \Rightarrow -30x=0 \\ \Rightarrow x=0 \end{gathered}$$

Substituting $x$ in equation $\left(1\right)$.

$$\begin{gathered} \Rightarrow y=5\left(0\right)-1 \\ \Rightarrow y=-1 \end{gathered}$$

Hence, the given system of equations has one solution is $\left(0,-1\right)$

Therefore, option $\left(A\right)$ is the correct answer.