Solve the following system of linear equations : 7 x

Q) Solve the following system of linear equations : 7 x – 2 y = 5 and 8 x + 7 y = 15 and verify your answer.

Ans: Given equations are:

7 x – 2 y = 5 …………………… (i)

8 x + 7 y = 15 …………………..(ii)

To get the value of variables, we need to first drop one variable.

Let’s multiply (i) by 7 and (ii) by 2 and add them up:

∴ 7 (7 x – 2 y) + 2 (8 x + 7 y) = 7 x 5 + 2 x 15

∴ 49 x – 14 y + 16 x + 14 y = 35 + 30

∴ 65 x = 65

∴ x = $frac{65}{65}$ = 1

Transferring value of x = 1 in equation (ii), we get:

7 x – 2y = 5

∴ 7 (1) – 2 y = 5

∴ 7 – 2 y = 5

∴ 7 – 5 = 2 y

∴ y = $frac{2}{2}$ = 1

Therefore, values of x and y are 1 each.

Verification:

To verify each equation, we need to find value of LHS and check if it matches with RHS or not.

Let’s start with LHS of equation (i): 7 x – 2 y = 5

LHS = 7 x – 2 y

= 7 (1) – 2(1)

= 7 – 2 = 5 = RHS

Hence, equation (i) is verified.

Next, let’s check LHS of equation (ii): 8 x + 7 y = 15 ..

LHS = 8 x + 7 y

= 8 (1) + 7 (1)

= 8 + 7 = 15 = RHS

Hence, equation (ii) is verified.

Thus both equations are verified.

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