if system -4x - 7y = 4 and -24x - 9y = -6 is to be solved using the addition method?

Question

by what constant should one of the equations be multiplied if the x terms are drop out?

Answer 1

(-4x - 7y = 4 (.-6)
(-24x - 9y = -6
==>
You must equal the terms of "x" to cancel, multiplying Equation 1 to -6:
(24x + 42y = -24
(-24x - 9y = -6
Addition:
24x -24x + 42y - 9y = -30
33y = -30
y = -10/11

-4x -7(-10/11) = 4
-4x +70/11 = 4
-4x = 4 - 70/11
-4x = -26/11
x = -26/11 : -4
x = -26/11 . -1/4
x = 13/22
Solution: {(13/22; -10/11)}

Answer 2

In order to have the x-term cancel out when you perform the addition, the two terms must be equal and of opposite signs.

So multiply the first equation by -6 giving:
24x +42y =-24
Now when you add the second equation the x terms will disappear. [24x + (-24x) =24x-24x =0]

Answer 3

Your x terms are -4 and -24. To make them the same, you must multiply the first equation by -24/-4, which happens to be 6. Your first equation is now

-24x - 42y = 24

Answer 4

I agree with the value of 6, except that I would multiply by -6 to solve by the addition method.

Answer 5

multiply the first equation by 6

-24x -42 y = 24 substract the second from this

you obtain -33y =30 y = -10/11

substituing this value you obtain x = -22/57

verify my calculations!

Answer 6

multiply (1) by -6
24x+42y=-24
-24x-9y=-6
adding
33y=-30
dividing by 33
y=-30/33
simplifying
y=-10/11
similarly multiplying (1) by -9 and (2) by 7
36x+63y=-54
-168x-63y=-42
adding
-132x=-96
dividing by -132
x=-96/-132
=8/11