Question

Solve using the given method
linear combination
3x + 2y = -4
4x - y = 13

Answer 1

The solution of the equation is : x= 2, y = -5

Explanation:

3x + 2y = -4..[1]

4x - y = 13..[2]

In the linear combination method, we multiply the equations with numbers to make the coefficients one variable the same but with opposite signs.

And after that, we add them and solve the reaming equation for the value of another variable.

So here, 1 × [1] +2 [2]

`1* 3x + 1* 2y =1* (-4}`

`2* 4x - 2* y =2* (13}`

`3x + 2y = -4`

`8x - 2y = 26`

`3x+8x=-4+26`

`11x=22`

`x=(22)/(11)=2`

Now, for value of y put value of x in any of the given equation:

4x - y = 13

4 × 2 - y =13

y = 8 - 13 = -5

The solution of the equation is : x= 2, y = -5

Answer 2

The solution is
`x=2, y=-5`

Explanation:

we have

`3x + 2y = -4` ----> equation A

`4x - y = 13` -----> equation B

Multiply the equation B by 2 both sides

`2*(4x - y)= 2*13`

`8x-2y= 26` -----> equation C

Adds equation A and equation C

`3x + 2y = -4\\ \\8x-2y= 26\\ \\----------\\ \\3x+8x+2y-2y=-4+26\\ \\11x=22\\ \\x=2`

Find the value of y

substitute the value of x in the equation A

`3(2)+ 2y = -4`

`2y=-4-6`

`2y=-10`

`y=-5`