Question

Use the linear combination method 2x + 3y = 11 -4x + 2y = 2

(1,3)
(2,3)
(1,2)
(1, -2)

Answer 1

(1,3) is the solution of the system of linear equations.

Explanation:

we are given system of linear equations as:

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

and -4x + 2y = 2------(2)

on solving the system of linear equations by the elimination method we have:

multiply equation (1) by 2 and add equation (1) and (2) we have:

4x+6y=22

-4x+2y=2

8y=24

⇒ y=3 ( since on dividing both sides by 8)

now on putting value of y in equation (1) we have:

2x+3×3=11

2x=11-9

2x=2

⇒ x=1

Hence, the solution is (1,3).

Answer 2

(1,3)

Explanation:

Given : 2x+3y=11 ---(a)

-4x+2y=2---(b)

Solution:

Multiply equation a by -2 both sides.

So, equation becomes : -4x-6y= - 22

Now , Subtract the equation b from resultant equation :

⇒(-4x-6y+22)-(-4x+2y-2)

⇒-4x-6y+22+4x-2y+2=0

⇒-8y+24=0

⇒-8y=-24

⇒
`y=(-24)/(-8)`

⇒y = 3

Now to find x put value of y in equation a

⇒2x+3*3=11

⇒2x+9=11

⇒2x=2

⇒x=1

Thus the solution is (x,y)=(1,3)