Question

Could you please answer this question?
Only answer question 26
The answers are: x = 5 y = -2

Answer 1

Question:

$3x - y = 17 \\ \\ \frac{x}{5} + \frac{y}{2} = 0$

Answer:

We have

$3x - y = 17 \: - - (1) \\ \texttt{and}\\ \frac{x}{5} + \frac{y}{2} = 0 - - (2)$

We will simplify eq(2)

$\rightarrow \frac{x}{5} + \frac{y}{2} = 0 \\ \\ \implies \frac{2x + 5y}{5 \times 2} = 0 \\ \\ \implies \frac{2x + 5y}{10} = 0 \\ \\ \implies \: 2x + 5y = 0$

Our equations are,

$\blue{3x - y = 17 } \\ \blue{2x + 5y = 0}$

• Using Elimination method

We will multiply first equation by 5 to make coefficient of y equal to the second equation.

$5 \times (3x - y = 17) \\ 1 \times (2x + 5y = 0) \\ \\ \implies \: 15x \: \cancel{- 5y} \: = 85 \\ \implies \: 2x \: \: \: \cancel{+ 5y } \: = 0 \\ \\ \implies17x = 85 \\ \\ \implies \: x = \frac{85}{17} \\ \\ \green{ \implies \: x = 5}$

Now we will substitute the value of x in 2x + 5y = 0 to find y.

$\implies \: 2x + 5y = 0 \\ \\ \implies \: 2(5) + 5y = 0 \\ \\ \implies10 + 5y = 0 \\ \\ \implies5y = - 10 \\ \\ \implies \: y = \frac{ - 10}{ \: \: 5} \\ \\ \green{ \implies \: y = - 2}$

Hence, x = 5 and y = -2