Question

solve by substitution method 15x+10y=45
9x+5y=24
​

Answer 1

Answer

${\sf \dashrightarrow 15x + 10y = 45 \: \: --- (i)}$

${\sf \dashrightarrow 9x + 5y = 24 \: \: --- (ii)}$

We should find the value of x by equation (i),

${\sf \dashrightarrow 15x + 10y = 45}$

${\sf \dashrightarrow 15x = 45 - 10y}$

${\sf \dashrightarrow x = \dfrac{45 - 10y}{15}}$

Now, we should find the value of y by second equation.

${\sf \dashrightarrow 9x + 5y = 24}$

${\sf \dashrightarrow 15 \bigg( \dfrac{45 - 10y}{15} \bigg) + 5y = 24}$

${\sf \dashrightarrow \dfrac{675 - 150y}{15} + 5y = 24}$

${\sf \dashrightarrow \dfrac{675 - 150y + 75y}{15} = 24}$

${\sf \dashrightarrow \dfrac{675 - 75y}{15} = 24}$

${\sf \dashrightarrow 675 - 75y = 24 \times 15}$

${\sf \dashrightarrow 675 - 75y = 360}$

${\sf \dashrightarrow -75y = 360 - 675}$

${\sf \dashrightarrow -75y = (-315)}$

${\sf \dashrightarrow y = \cancel \dfrac{-135}{-75} = \dfrac{27}{15}}$

Now, we should find the original value of x by equation (i)

${\sf \dashrightarrow 15x + 10y = 45}$

${\sf \dashrightarrow 15x + 10 \bigg( \dfrac{27}{15} \bigg) = 45}$

${\sf \dashrightarrow 15x + \dfrac{270}{15} = 45}$

${\sf \dashrightarrow 15x = 45 - \dfrac{270}{15}}$

${\sf \dashrightarrow 15x = \dfrac{675 - 270}{15}}$

${\sf \dashrightarrow 15x = \dfrac{405}{15}}$

${\sf \dashrightarrow 15x = 27}$

${\sf \dashrightarrow x = \dfrac{27}{15}}$

Hence, the values of x and y are $\sf \dfrac{27}{15}$ and $\sf \dfrac{27}{15}$ respectively.