Question

solve 2x+3y=11 and 2x-4y=-24 and hence find the value of 'm' for which y=mx+3

Answer 1

2x + 3y = 11   ------------- [ 1 ]

2x - 4y = -24------------- [ 2 ]

[ 1 ] - [ 2 ]:

3y - ( - 4y) = 11 - ( -24)

3y + 4y = 11 + 24

7y =35

y = 5

Solve x:

Sub y = 5 into equation [ 1 ]:

2x + 3(5) = 11

2x + 15 = 11

2x = 11 - 15

2x = -4

x = -2

FInd y = mx + 3:

Sub y = 5 and x = -2

5 = m(-2) +3

5 = -2m + 3

-2m = 2

m = -1

Answer: m = -1

Answer 2

Answer:

$\\ \tt \: 2x + 3y = 11 \qquad \quad \: (1) \\ \\ \tt \: 2x - 4y = - 24 \qquad \quad \: (2)$

From equation (1), we obtain -

$\\ \tt \: x = \frac{11 - 3y}{2} \qquad \quad \: (3)$

Substituting this value in equation (2), we obtain -

$\\ \tt \: 2 \: \bigg( \frac{11 - 3y}{2} \bigg) \: - 4y = - 24 \\ \\ \\ \implies \tt \: 11 - 3y - 4y = - 24 \\ \\ \\ \implies \tt \: - 7y = - 35 \\ \\ \\ \implies \tt \: \frac{ - 35}{ - 7} \\ \\ \\ \implies \tt{ \blue{y = 5}} \qquad \quad \:( 3)$

Putting this value in equation (3), we obtain -

$\\ \tt \: x = \frac{11 - 3 \times 5}{2} = \frac{4}{2} = - 2 \\ \\ \\ \bf{ \green{Hence, \: x = - 2 \: \: and \: \: y = 5}} \\ \\ \implies \tt \: y = mx + 3 \\ \\ \\ \implies \tt \: 5 = m \times - 2 + 3 \\ \\ \\ \implies \tt{ \red{m = - 1}}$