Verified answer

Answer:

Given:-

• Two linear equations
• 2x + 3y = 11
• 2x - 4y = -24

• y = mx + 3

To Find:-

• The value of m

Solution:-

We have linear equations

2x+3y = 11........(1)

2x - 4y = -24........(2)

y = mx + 3.........(3)

Subtracting (2) from (1):-

i.e, (1) - (2):-

[tex]\implies[/tex] 2x + 3y - (2x - 4y) = 11 -(-24)

[tex]\implies[/tex] 2x + 3y - 2x + 4y = 11 + 24

[tex]\implies[/tex] 7y = 35

[tex]\implies[/tex] y = [tex]\frac{35}{7}[/tex]

[tex]\implies[/tex] y = 5

Substitute y = 5 in (1)

[tex]\implies[/tex] 2x + 3(5) = 11

[tex]\implies[/tex] 2x + 15 = 11

[tex]\implies[/tex] 2x = -4

[tex]\implies[/tex] x = -2

Substitute x = 2 and y = 5 in (3)

[tex]\implies[/tex] y = mx + 3

[tex]\implies[/tex] 5 = m(-2) + 3

[tex]\implies[/tex] m = -1

[tex] \implies\big \underline{ \boxed{ \sf \bold{ \therefore The \: value \: of \: m \: = -1}} }[/tex]

Answer:

• The value of m is -1.

Step-by-step explanation:

Let,

• 2x+3y=11 -----(eqn 1)

• 2x-4y=-24 ---(eqn 2)

• y=mx+3 -------(eqn 3)

Subtract eqn 2 from eqn 1-

➪ 2x+3y - (2x-4y) = 11-(-24)

➪ 2x+3y-2x+4y = 11+24

➪ 7y = 35

➪ y = 35/7

➪ y = 5

Substitute y=5 in eqn 1.

➪ 2x+3y=11

➪ 2x + 3(5) = 11

➪ 2x + 15 = 11

➪ 2x = -4

➪ x = -4/2

➪ x = -2

Substitute x=-2 and y=5 in eqn 3.

➪ 5 = m(-2) + 3

➪ 5 = -2m + 3

➪ 5-3 = -2m

➪ 2 = -2m

➪ 2/-2 = m

➪ -2/2 = m

➪ -1 = m

➪ m = -1