Question

3x-5y=16; x-3y=8, Solve the set of simultaneous equations.

Answer 1

3x - 5y = 16 -------(1)

x - 3y = 8

=> 3x - 9y = 24 -----(2)

On subtracting equation 1 from 2, we get

-9y + 5y = 24 - 16

=> - 4y = 8

=> y = - 2

Now,

On substituting the value of y in equation 1, we get

3x - 5(-2) = 16

=> 3x + 10 = 16

=> 3x = 6

=> x = 2

Answer 2

Answer:

After solving the given equations we get,

x=2 and y=-2

Step-by-step explanation:

Given: $3x-5y=16; x-3y=8$

We have to solve the above equations.

We are solving in the following way:

We have,

$3x-5y=16\ \ ...1)\\x-3y=8\ \ ..2)$

Multiplying the second equation by -3, then adding the equations together:

$\begin{array}{l}(3 x-5 y=16) \\-3(x-3 y=8)\end{array}$

Becomes:

$\begin{array}{l}3 x-5 y=16 \\-3 x+9 y=-24\end{array}$

Adding these equations to eliminate x:

$4 y=-8$

$\text { Then solving } 4 y=-8 \text { for } y \text { : }$

$\begin{array}{l}4 y=-8 \\\frac{4 y}{4}=\frac{-8}{4} \\y=-2\end{array}$

Hence, we get the value of y is -2.

Now, putting the value of y in the equation$3 x-5 y=16$ we get,

$3 x-(5)(-2)=16\\3 x+10=16\\3 x=16+-10\\\begin{array}{l}3 x=6 \\\frac{3 x}{3}=\frac{6}{3} \\x=2\end{array}$

Hence, we get, x=2 and y=-2