Question

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

Answer 1

Answer:

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

Step-by-step 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

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

$2y=-4-6$

$2y=-10$

$y=-5$

Answer 2

Answer:

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

Step-by-step 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]

$1\times 3x + 1\times 2y =1\times (-4}$

$2\times 4x - 2\times y =2\times (13}$

$3x + 2y = -4$

$8x - 2y = 26$

  $3x+8x=-4+26$

$11x=22$

$x=\frac{22}{11}=2$

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