Question

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Answer 1

QUESTION:

Solve the equation:

• 2x + 3y = 9
• 3x + 4y = 5

ANSWER:

• The values of x = - 21

• The values of y = 17

GIVEN:

• 2x + 3y = 9

• 3x + 4y = 5

TO FIND:

• The values of x and y.

EXPLANATION:

METHOD 1:

2x + 3y = 9------>1

3x + 4y = 5-----> 2

Multiply by 3 on both sides of equation 1.

6x + 9y = 27 -------> 3

Multiply by 2 on both sides of equation 2.

6x + 8y = 10-------> 4

Subtract equation 3 and 4

$\sf 6x + 9y = 27 \\ \\ \sf 6x + 8y = 10 \\\sf ( - ) \ \ ( - ) \ \ \ ( - ) \\ \underline{ \qquad\qquad\qquad} \\\sf 0 \ + y \ \ \ = 17 \\ \underline{ \qquad\qquad\qquad}$

Substitute y = 17 in equation 1

2x + 3(17) = 9

2x = 9 - 51

2x = - 42

x = - 21

HENCE THE VALUE OF X = - 21 AND Y = 17.

VERIFICATION:

Substitute x = - 21 and y = 17 in equation 2

3( - 21) + 4(17) = 5

- 63 + 68 = 5

5 = 5

HENCE VERIFIED.

METHOD 2:

2x + 3y = 9

2x = 9 - 3y

x = (9 - 3y) / 2

Substitute x = (9 - 3y)/2 in 3x + 4y = 5

3((9 - 3y)/2) + 4y = 5

Multiply by two on both sides.

3(9 - 3y) + 8y = 10

27 - 9y + 8y = 10

- y = 10 - 27

y = 17

Substitute y = 17 in 3x + 4y = 5

3x + 4(17) = 5

3x + 68 = 5

3x = 5 - 68

3x = - 63

x = - 21

HENCE THE VALUE OF X = - 21 AND Y = 17.