math problem! has to do with solving a system: such as susbtitution or linear combination...?

Question

okay i been working for 45 minutes on this problem and i can't solve it! can someone help me? it says: "Solve the method by your choice"

5x+2y=4
3x-5y=-1

Please help me!

Answer 1

5x+2y=4
3x-5y=-1
Multiply top equation by 3 and bottom by -5
(5x+2y=4)*3
(3x-5y=-1)*-5
15x+6y=12
-15x+25y=5
Add them together
31y=17
y = 17/31
Plug it in to the first equation
5x+2y=4
5x+2(17/31)=4
5x= 4 - (34/31)
5x = (124 - 34) / 31
5x = 90/31
x = 90/31 * 1/5
x = 90/155
x = 18/31 (y=17/31)
Plug both into second equation
3x-5y=-1
3*(18/31) - 5*(17/31) = -1
Multiply by 31
3*18 - 5*17 = -31
54 - 95 = -31
-31 = -31 CHECK

Answer 2

I would use the addition method, sometimes called the elimination method. You add the two equations together, but one of the variables has to fall out. So the number in front of the variables have to be opposites, meaning one positive and one negative. It is legal in math to multiply a whole equation by the same number. I would multiply the first equation by 5 and the second equation by 2. So the y will fall out because you will have a positive 10y and a negative 10y.

25x+10y=20
6x - 10y =-2
Add
31x = 18 or x = 18/31
Substitute 18/31 back into either original equations
5(18/31) +2y =4
90/31 +2y =4
2y=4-90/31
2y=34/31
y=17/31
Check to make sure it works in both and it does.
(18/31, 17/31)

Answer 3

5x+2y=4 and 3x-5y=-1
so 3x=5y-1 and then x=5/3y-1/3
and 5x=4-2y so x=4/5-2/5y
so 5/3y-1/3 = 4/5-2/5y then choose a common denominator of 15 and multiply the left side by 5/5 and the left side by 3/3
25/15y-5/15 = 12/15-6/15y and then move y to the left.
31/15y=17/15 - the 15s can be cancelled out and y = 17/31
Substitute in to solve for x.
x = 18/31

Answer 4

i actually could get ultimate answer for this: nicely there are 4 procedures you're able to do it, a million. you could replace in via fixing for one variable, and then putting it into the 2d equations. 2. you could graph it and locate the x,y intercept. 3. in case you have a graphing calculator, you need to use the simult equations solver, punch in each and every formula, and it provide you with the values. 4. or you need to use a matrix to unravel it. Like this: set up the intial equation like this. 3 -4 21 4 2 6 you may do a series of math applications to alter the equation to the matrix type a million 0 x 0 a million y this provide you with your answer. so which you initiate with 3 -4 21 (first divide the 1st row via 3) 4 2 6 a million -(4/3) 21 (now mult this row via -4 and upload it to the backside) 4 2 6 a million -(4/3) 21 0 (22/3) -22 (now divide this row via (22/3) a million -(4/3) 21 0 a million -3 (now multi this row via -(4/3) and upload it to the suitable) a million 0 3 0 a million -3 it fairly is your answer x = 3, y = -3. I

Answer 5

for the first equation (1)
5x=4-2y
x=(4-2y)/5 (a)
from (2)
3x=5y-1
x=(5y-1)/3 (b)
then from (a) and (b)
(4-2y)/5=(5y-1)/3
then
3(4-2y)=5(5y-1)
I guess you can follow on.
once you have the value for y, substitute than on (a) and you get x

Answer 6

5x+2y=4 mul by 5 -> 25x+10y=20 ---- (1)
3x-5y=-1 mul by 2 -> 6x-10y=-2 -------(2)

adding (1) and (2) gives
31x=18
x=18/31

subst x in any eqn u get y=17/31

Answer 7

1. multiply the 1st eq by (3)
2. multiply the 2nd eq by (-5)
3. then add the two

15x + 6y = 12
-15x + 25y = 5

31y = 17
y = 17/31

Answer 8

25x + 10y = 20
6x - 10y = - 2-----ADD
31x = 18
x = 18/31

90/31 + 2y = 4
2y = 124/31 - 90/31
2y = 34/31
y = 17/31

SOLUTION
x = 18/31 , y = 17/31

Answer 9

5x+2y=4
3x-5y=-1

5y=3x+1
y=3/5x +1/5

5x+2y=4
5x+2(3/5x+1/5)=4
5x+6/5x+2/5=4
31/5x+2/5=4
31/5x=18/5
31x=18
x=18/31

3x-5y=-1
3(18/31)-5y=-1
54/31-5y=-1
5y=85/31
y=17/31

(18/31,17/31)