Q3. - Algebra 2

Question

If $\mathbf{3}\mathbf{x}-\mathbf{y}=-\mathbf{3}$and $\mathbf{x}+\mathbf{5}\mathbf{y}=\mathbf{15},$ what is the value of $\mathbf{y}?$

(A) -3

(B) 0

(C) 1

(D) 3

Step-by-Step Solution

Answer

The value of $y$ is $\left(D\right)3.$

Step 1 – Write the given equations

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

Step 2 – Apply the basic math operations on equations

Multiplying equation (2) by 3, we get

$3x+15y=45$

It can be rewritten as follows,

$3x+15y-45=0 ....\left(3\right)$

Step 3 – Subtract equation (1) from equation (3)

Subtracting equation (1) from (3), we get

$\begin{array}{c}(3x+15y-45)-(3x-y+3)=0\\ 3x+15y-45-3x+y-3=0\\ 16y-48=0\\ 16y=48\\ y=\frac{48}{16}\\ y=3\end{array}$

Thus, the value of $y$ is 3.