Question

1/5y=22-1/4x and 1/5x=23-1/4y find the values of x and y..linear equations in 2 variables

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

x=40 and y=60

Step-by-step explanation:

Value of (1)

$\frac{1}{5} y + \frac{1}{4} x = 22\\ \frac{4y+ 5x}{20} = 22 \\ 4y + 5x = 22 \times 20 \\ 4y + 5x = 440$

Value of (2)

$\frac{1}{5} x + \frac{1}{4} y = 23 \\ \frac{4x + 5y}{20} = 23 \\ 4x + 5y = 460$

Multiplying (1) by 5 and (2) by 4 we get

$5(4y + 5x = 440) \: \: \: \: (1) \\ 4(4x + 5y = 460) \: \: \: (2)$

Substracting (2) from (1) we get

$(20y + 25x = 2200) - (16x + 20y = 1840) \\ 25x - 16x = 2200 - 1840 \\ 9x = 360 \\ x = \frac{360}{9} \\ x = 40$

Now taking the value of y while putting the value of x=40

$5x + 4y = 440 \\ 5 \times 40 + 4y = 440 \\ 200 + 4y = 440 \\ 4y = 440 - 200 \\ 4y = 260 \\ y = \frac{260}{4} \\ y = 60$

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