x + 2y = 5, 3x + 4y = 1?

x + 2y = 5......(1)
3x + 4y = 1....(2)

(1) x 3: 3x + 6y = 15....(3)
(2) x 1: 3x + 4y = 1......(4)

Subtract equation (4) from equation (3)
(3x - 3x)+(6y - 4y)= (15-1)
2y = 14
y = 14/2
y = 7

Substitute the value of y into equation (1).
x + 2y = 5
x + 2(7) = 5
x + 14 = 5
x = 5-14
x = -9

SOLUTION: (x, y) = (-9, 7)

Relative values of y in relation to x:
x + 2y = 5
2y = 5 - x
y = (5 - x)/2

3x + 4y = 1
4y = 1 - 3x
y = (1 - 3x)/4

Value of x:
4(5 - x) = 2(1 - 3x)
2(5 - x) = 1 - 3x
10 - 2x = 1 - 3x
x = - 9

Value of y:
= (5 - [- 9])/2
= (5 + 9)/2
= 14/2
= 7

Answer: x = - 9, y = 7

Proof (1st equation):
- 9 + 2(7) = 5
- 9 + 14 = 5
5 = 5

Proof (2nd equation):
3(- 9) + 4(7) = 1
- 27 + 28 = 1
1 = 1

removing by addition approach 4x + 2y = 5- - - - -Equation a million 3x - 4y = a million- - - - - Equation 2 - - - - - - - - - Multiply equation a million by 2 4x + 2y = 5 2(4x) + 2(2y) = 2(5) 8x + 4y = 10 combine this equation with equation 2 - - - - - - - - - - removing of y 8x + 4y = 10 3x - 4y = a million - - - - - - - - - - 11x = 11 Divide the two components of the equation by 11 11x / 11 = 11 / 11 x = 11/11 x = a million substitute the x fee into equation a million - - - - - - - - - 4x + 2y = 5 4(a million) + 2y = 5 4 + 2y = 5 Transpose 4 4 + 2y - 4 = 5 - 4 2y = a million Divide the two components of the equation by 2 2y / 2 = a million / 2 y = a million/2 substitute the y fee into equation a million - - - - - - - - - - examine for equation a million 4x + 2y = 5 4(a million) + 2(a million/2) = 5 4 + 2/2 = 5 4 + a million = 5 5 = 5 - - - - - - - - - examine for equation 2 3x - 4y = a million 3(a million) - 4(a million/2) = a million 3 - 4/2 = a million 3 - 2 = a million a million = a million - - - - - - - - - the two equations stability the answer set (a million, a million/2) - - - - - - - -s-

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

x + 2y = 5
-2(x + 2y) = -2(5)
-2x - 4y = -10

...-2x - 4y = -10
+ 3x + 4y = 1 (addition)
--------------------------
x = -9

x + 2y = 5
-9 + 2y = 5
2y = 5 + 9
2y = 14
y = 14/2
y = 7

∴ x = -9 , y = 7

- 2x - 4y = - 10
3x + 4y = 1------ADD

x = - 9

- 9 + 2y = 5
2y = 14
y = 7

x = - 9 , y = 7

Multiply each value in the first equation by 2 so that you have +4y so both y values are the same.

2x+4y=10

Now you have

2x+4y=10
3x + 4y = 1

Because they are both positive you minus the equations

-x=9
x=-9

Substitute the x value (-9) into any one of these equations.

2(-9)+4y=10

-18+4y=10

Add 18 to both sides

4y=28

Divide both sides by 4

y=7

x=-9, y=7

* 19 minutes ago

X= -9, Y=7

here is how I got the solution:

x + 2y = 5
x = 5 - 2y

3x + 4y = 1
3(5 - 2y) + 4y = 1
15 - 6y + 4y = 1
-2y = -14
y = -14 / -2
y = 7

3x + 4y =1
3x + 4 (7) = 1
3x + 28 = 1
3x = 1 - 28
3x = -27
x = -27/3
x = -9

first you need to multiply the first equation by -3 that way when you add the equations one of the variables cancels out, (the point is to end up defining one variable) So. -3(x+2y) = -3(5) or -3x -6y = -15
now add the two equations together(combining like terms and variables)
3x + 4y = 1
+ -3x - 6y = -15
============
0 + -2y = -14
or -2y = -14 so y=7
now plug seven into one of the equations to get x.
3x + 4(7) = 1
3x + 28 = 1
3x = -27
x = -9
so now that you have an x and y present it as an ordered pair
(x,y) so (-9,7)
Hope I helped!

So you asked for the elimiantion method NOT the substitution method:

Multiply each value in the first equation by 2 so that you have +4y so both y values are the same.

2x+4y=10

Now you have

2x+4y=10
3x + 4y = 1

Because they are both positive you minus the equations

-x=9
x=-9

Substitute the x value (-9) into any one of these equations.

2(-9)+4y=10

-18+4y=10

Add 18 to both sides

4y=28

Divide both sides by 4

y=7

x=-9, y=7

I'm bad at math. Just warning you. but here's my best shot, hopefully if I show all the steps I won't get it wrong:
I chose x to substitute first: x=5-2y

3(5-2y)+4y=1 so then...
15-6y+4y=1
15-2y=1
-2y=1-15
-2y=-14
y=7

so then I put y=7 into the first problem to find x.
x=5-2y
x=5-2(7)
x=5-14
x=-9
So then if those calculations are correct, your coordinates would be (-9,7)

I see someone else answered, but maybe you'll find one method or the other easier to understand or work through :)