x = 1/5y, 3x + 2y =26?

y=10, x=2

x in terms of y—2nd equation:
3x + 2y = 26
x = (26 - 2y)/3

Value of y:
3(1/5y) = 26 - 2y
3/5y = 26 - 2y
3y = 130 - 10y
13y = 130
y = 10

Value of x (1st equation):
= 1/5(10)
= 10/5 or 2

Answer: x = 2, y = 10

Proof (2nd equation):
3(2) + 2(10) = 26
6 + 20 = 26
26 = 26

5 x - y = 0
3 x + 2 y = 26

10 x - 2 y = 0
3 x + 2 y = 26-------ADD

13 x = 26
x = 2

6 + 2 y = 26
y = 10

x = 2 , y = 10

x = [1/5(y)] ...... (1)
3x + 2y = 26

3x + 2y = 26

Substitute (1) for x.
3[1/5(y)] + 2y = 26
3y/5 + 2y = 26
5(3y/5 + 2y) = 5(26)
3y + 10y = 130
13y = 130
y = 130/13
y = 10

x = 1/5(y)

Substitute 10 for y.
x = 1/5(10)
x = 10/5
x = 2

Check:
x = 1/5(y) (x = 2, y = 10)
3x + 2y = 26

Substitute 2 and 10 for x and y respectively.

2 ≟ 1/5(10)
2 ≟ 10/5
2 = 2 ✔

3(2) + 2(10) ≟ 26
6 + 20 ≟ 26
26 = 26 ✔

∴ x = 2, y = 10

Use x=1/5y to substitute into the next equation, 3x+2y=26.

So we have 3*(1/5y) + 2y = 26
3/5y + 2y = 26
13/5y = 26
13y = 130
y = 10

Now that you have y, use it in the original expression x=1/5y to obtain x.

x = 1/5*10
x = 2

Now check your answers.

2 = 1/5*10 correct!
3*2 + 2*10 = 26
6 + 20 = 26
26 = 26 correct!

plug the value of x = 1/5y in the second equation

3 ( 1/5y ) + 2y = 26
(3y + 10 y)/5 =26
13y / 5 = 26
y= 10
x = 1/5 y = 10 /5 = 2
thus x = 2 and y =10

1) x = y/5 {or do you really mean 1/(5y)?}

2) 3x + 2y = 26

3(y/5) + 2y = 26 {substitute for x from equation 1}

3y/5 + 10y/5 = 26

13y/5 = 26

y = (5/13)(26)

y = 10

1) x = 10/5

x = 2

check

3(2) + 2(10) = 26

6 + 20 = 26

26 = 26

Does x = 1/(5y) or does x = (1/5)y?

x = (1/5)y

3(1/5)y + 2y = 26
(3/5)y + 2y = 26
3y + 10y = 130
13y = 130
y = 10

x = (1/5)y = 2

3 * 2 + 2 * 10 = 6 + 20 = 26


x = 1/(5y)

3(1/(5y)) + 2y = 26
3/(5y) + 2y = 26
3 + 10y^2 = 26y
10y^2 - 26y + 3 = 0

y = (26 +/- sqrt((-26)^2 - 4 * 10 * 3)) / (2 * 10)
y = (26 +/- sqrt(676 - 120)) / 20
y = (26 +/- sqrt(556)) / 20
y = (26 + sqrt(556)) / 20 or y = (26 - sqrt(556)) / 20
y = 2.48 or y = 0.12

y = 5x
3x + 10x = 26
13x = 26
x= 2
y= 5x = 10
checking:
x=2 and y =10
y/5 = 10/5 = 2 = x
3x+2y = 3(2) + 2(10) = 26
hence true

y=10
x=2

3*2 = 6
2*10 = 20
6+20=26
hope that helps