Question

x+4y=45;–3+5y=120 find the solution set​

Answer 1

Given Equation Are :-

• x+4y=45 _____(1)
• -3x+5y= 120. _____(2)

Multiplying equation (1) with 5 we get,

${\implies \sf(5 \times x) + (5 \times 4y) = 45 \times 5}$

${\implies \sf5x+ 20y=225} \: \: \: \: \: - - - (3)$

Multiple Equation (2) with 4 we get,

${\implies \sf - 3x \times 4 + 5y \times 4 = 120 \times 4}$

${\implies \sf - 12x +20y = 480}\: \: \: \: \: - - - (4)$

Subtracting equation (4) from (3), we get

• $\sf \: \: \: \: \: 5x + 20y = 225 \\ \sf - 12x + 20y = 480 \\ \underline{ \sf \: + \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: = - \: \: \:} \\ \sf - 17x \: \: \: \: \: \: \: \: \: \: = - 225 \\ \sf \: x = \frac{225}{17} \\ \: \sf \ \: \: \: \: x = 15 \: \: \: \: \: \: \: \:$

Substituting x= 15 in Equation (1) We get,

$\implies \sf \: 15 + 4y = 45 \\ \implies \sf \: 4y = 45 - 15 \\\implies \sf4y = 30 \: \: \: \: \: \: \: \: \: \: \\\implies \sf \: y = \frac{30}{4} \: \: \: \: \: \: \: \: \\\implies \sf y = \frac{15}{2} \: \: \: \: \: \: \: \:$

• $\underline{\green{ \boxed{\sf \: Correct \: Answer= \left(15 , \dfrac{15}{2} \right)}}}$