Question

Determine the solution of the following systems of equation

8x+10y=4;11x+13y=4​

Answer 1

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$&#10148$ Given two equaton

$&#10148$ 8x + 10y = 4 ----------(1)

$&#10148$ 11x + 13y = 4 ----------(2)

• we can write the first eq. to common 2

$&#10148$ 4x + 5y = 2 ------------(3)

Now multiply with 11 to 3rd equaton and 4 to 2nd equaton

$&#10148$ 44x + 52y = 16 ————— (4)

$&#10148$ 44x + 55y = 22 —————(5)

• Now substract 4th eq. from 5th eq.

$\implies \: \: 3y = 6 \: \: \\ \\ \implies \: \: y = \frac{\cancel6}{\cancel3} \: \: \: \\ \\ \implies \: \: y = 2 \: \: \:$

Now putting the value of y in eq. 3rd

$\implies \: \: 4x + 5(2) = 2 \\ \\ \implies \: \: 4x = 2 - 10 \: \: \: \\ \\ \implies \: \: x = \frac{ - \cancel8}{\cancel4} \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \: x = - 2 \: \: \: \: \: \: \: \: \: \: \:$

• The value of x is -2 and y is 2 ..