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Question

Identify the correct answer which satisfies the linear equations: $$3x + 7y = 14$$ and $$2x + 7y = 21$$


A
(7,5)
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B
(7,5)
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C
(7,5)
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D
(7,5)
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Solution

The correct option is A $$(-7, 5)$$
$$3x + 7y = 14$$ ----- (1)
$$2x + 7y = 21$$ ----- (2)
Substitute the values of first option $$x = -7$$ and $$y = 5$$ in equations 1 and 2
$$3(-7) + 7(5) = 14$$
$$-21 + 35 = 14$$
$$14 = 14$$
$$2(-7) + 7(5) = 21$$
$$-14 + 35 = 21$$
$$21 = 21$$
Therefore, the first option satisfied the linear equations.
Likewise substitute the value of second option $$x = 7, y = 5$$
$$3(7) + 7(5) = 14$$
$$21 + 35 = 14$$
$$56 \neq 14$$
$$2(7) + 7(5) = 21$$
$$14 + 35 = 21$$
$$49 \neq 21$$
Similarly, check the options to satisfy the linear equation.
Here, the first option satisfied the linear equation.
The solution is $$(-7, 5)$$

Mathematics

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