algebra prob2?

Question

4x+3y = 2 and 5x-7y = -19

I already know that x=-1 and y=2 but if you know how, please find the answer(in an algebraic equation) to each of the expressions above and explain the processes thoroughly. Serious answers please. Thank you

why do you multiply everything on the first equation by 7 and the second equation by 3?


what do you do and why so to get -43 and 43?

Answer 1

why do you multiply everything on the first equation by 7 and the second equation by 3?

look at the y-terms in the 1st and 2nd equations
+3y
-7y
You want to eliminate the y-variable, so you multiply the
first equation by 7 and the second by 3, you get
+3y * 7 = +21y
-7y * 3 = -21y
now, add them together: +21y - 21y = 0

Answer 2

it's called linear combination
you multiply the first equation by 7 and the second by 3 so that at least one set of like terms are opposites
multiplying the first equation by 7 makes the y value, 3y, 21y
multiplying the second equation by 3 makes the y value, -7y,-21y
when you add the 2 equations vertically, the y terms are cancelled out

Answer 3

Addition method works by eliminating a variable through addition of opposites

We mult. by 7 to produce 28x + 21y = 14 and
we mult. by 3 to produce 15x - 21y = -57 so y terms will cancel

43 x = -43 and x = -1 then substitue into either or both of the equations to get y

4(-1) + 3y = 2 and -4 + 3y = 2 so 3y = 6 and y = 2

Answer 4

Hello,
Multiply the first one by -5 giving us -20x -15y = -10

Multiply the second one by 4 giving us 20x -28y = -76 now add them together and we get -43y = -86 and divide by -43 giving us y = 2. Putting this back into the first one give us.

4x +3*(2) = 2 or 4x + 6 = 2 and then 4x = -4 so x = -1.

Hope This Helps!

Answer 5

4x + 3y = 2 . . . . . . equation 1
5x - 7y = - 19 . . . . . equation 2
x = (7y - 19)/5 . . . . substitute to 1
4(7y - 19)/5+ 3y = 2
(28y - 76) + 15y = 10
43 y = 86
y = 2
x = [ 7(2) - 19 ] / 5 = 1