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

Explanation:

Find the value of any one variable in the form of another from the equation first.

Then put that value in the second equation and solve.

2x+3y=11

⇒2x=11-3y

⇒x=1/2(11-3y)....(1)

Put this value of x in the second equation.

2[1/2(11-3y)]-4y=-24

⇒11-3y-4y=-24

⇒11-7y=-24

⇒11+24=7y

⇒35/7=y

⇒y=5

Now put the value of y in equation (1)

x=1/2(11-3×5)

⇒x=1/2×-4

⇒x=-2

Put the value of x and y in y=mx+3 to find the value of m

⇒5=m×(-2)+3

⇒5-3=-2m

⇒2=-2m

⇒m=-1

Final Answer:

Hence, the value of x,y,m are -2,5,-1 respectively.