Question

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

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Answer 1

$\huge\underbrace\mathfrak\color{lime}{ †\: Question:–}$

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

$\huge\underbrace\mathfrak\color{lime}{ †\: Answer:–}$

$~~~~~~~~~~~\huge\longrightarrow$$\bold{2x + 3y = 11}$ -------(1)

$~~~~~~~~~~~\huge\longrightarrow$$\bold{2x - 4y = -24}$ -------(2)

From equation (2) We have ;

$~~~~~~~~~~~~\longrightarrow$$\bold{2x - 4y = -24}$

$~~~~~~~~~~~~\longrightarrow$$\bold{2x = - 24 + 4y}$

$~~~~~~~~~~~~\longrightarrow$$\bold{x = \frac{-24 + 4y}{2}}$

$~~~~~~~~~~~~\longrightarrow$$\bold{x = - 12 + 2y}$ ----------(3)

Substitute eq(3) in eq(1)

$~~~~~~~~~~~~\longrightarrow$$\bold{2x + 3y = 11}$

$~~~~~~~~~~~~\longrightarrow$$\bold{2( -12 + 2y) + 3y = 11}$

$~~~~~~~~~~~~\longrightarrow$$\bold{ - 24 + 4y + 3y = 11}$

$~~~~~~~~~~~~\longrightarrow$$\bold{7y = 11 + 24}$

$~~~~~~~~~~~~\longrightarrow$$\bold{7y = 35}$

$~~~~~~~~~~~~\longrightarrow$$\bold{y = \frac{35}{7}}$

$~~~~~~~~~~~~\longrightarrow$$\bold{y = 5}$

Substitute y = 5 in eq(3)

$~~~~~~~~~~~~\longrightarrow$$\bold{x = -12 + 2(5)}$

$~~~~~~~~~~~~\longrightarrow$$\bold{x = -12 + 10}$

$~~~~~~~~~~~~\longrightarrow$$\bold{x = - 2}$

The solution is y = 5 and x = - 2

$~~~~~~~~~~~~~y = mx + 3$

$~~~~~~~~~~~~\longrightarrow$$\bold{5 = m(-2) + 3}$

$~~~~~~~~~~~~\longrightarrow$$\bold{5 = -2m + 3}$

$~~~~~~~~~~~~\longrightarrow$$\bold{5 - 3 = - 2m}$

$~~~~~~~~~~~~\longrightarrow$$\bold{2 = - 2m}$

$~~~~~~~~~~~~\longrightarrow$$\bold{\frac{2}{-2} = m}$

$~~~~~~~~~~~~\longrightarrow$$\bold{\cancel\frac{2}{-2} = m}$

$~~~~~~~~~~~~\longrightarrow$$\bold{m = - 1}$

So the answer for the solution y = mx + 3 Is

m = - 1

Answer 2

Step-by-step explanation:

Using elimination method

2x + 3y = 11

-2x - 4y = -24

-------------------

7y = 35

y = 35/7

y = 5

when y = 5

2x+3(5)=11

2x=11-15

x = -4/2

x = -2

when x = -2 and y = 5

y = mx + 3

5 = m (-2) + 3

5-3 = -2m

2 = -2m

2/-2 = m

-1 = m

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