Question

Elimination_4x_2y=14 _10x+7y=_24

Answer 1

Answer:

The answer is $x=-\frac{50}{8}$  and $y=\frac{11}{2}.$

Step-by-step explanation:

Given:

-4x-2y=14

-10x+7y=-24

Now, to solve it by elimination:

$-4x-2y=14$   ......(1)

$-10x+7y=-24$ ......(2)

So, we multiply the equation (1) by 7 we get:

$-28x-14y=98$

And, we multiply the equation (2) by 2 we get:

$-20x+14y=-48$

Now, adding both the new equations:

$-28x-14y+(-20x+14y)=98+(-48)$

$-28x-14y-20x+14y=98-48$

$-28x-20x-14y+14y=50$

$-8x=50$

Dividing both the sides by -8 we get:

$x=-\frac{50}{8}$

Now, putting the value of $x$ in equation (1):

$-4x-2y=14$

$-4(-\frac{50}{8})-2y=14$

$\frac{200}{8} -2y=14$

$25-2y=14$

Subtracting both sides by 25 we get:

$-2y=-11$

Dividing both sides by -2 we get:

$y=\frac{11}{2}$

Therefore, the answer is $x=-\frac{50}{8}$  and $y=\frac{11}{2}.$