The solution of the pair of linear equations x + 2 y = 5 and 7 x + 3 y = 13 is (2, 1). Options: A . &nbspTrue B . &nbspFalse C . &nbspa=−3, b=+2, c=−7 D . &nbspa=−3, b=−2, c=−7

The solution of the pair of linear equations x+2y=5 and 7x+3y=13 is (2

Question

The solution of the pair of linear equations

x + 2 y = 5

and

7 x + 3 y = 13

is (2, 1).

Options:

A . True

B . False

C . a=−3, b=+2, c=−7

D . a=−3, b=−2, c=−7

Answer: Option B
:
B

x + 2 y = 5

...(1)

7 x + 3 y = 13

...(2)
Let's solve these equations using elimination method.
Onmultiplying the first equation by 7, we get

7 x + 14 y = 35

...(3)
On subtracting (2) from (3), we have

7 x + 14 y = 35

- 7 x - 3 y = - 13

_______________

11 y = 22

\Rightarrow y = 2

On subsituting value of y in

x + 2 y = 5

, we get

x + 2 (2) = 5

\Rightarrow x = 1

\Rightarrow x = 1

and

y = 2

Hence, the solution of the given equations is (1, 2).

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