Question

x/2+y=4/5. x+y/2=7/10

Answer 1

Answer:

x = 2/5

y = 3/5

Step-by-step explanation:

**Disclaimer** Hi there! I assumed the question to be a system of equations. The following answer is a method for solving a system of equations. Thus, if it is not, please let me know and I will modify my answer.

Given information:

$\frac{x}{2}+y=\frac{4}{5}$

$x+\frac{y}{2} =\frac{7}{10}$

Eliminate fractions by multiplying 10 on both sides of the first equation:

$10*\frac{x}{2}+10*y=10*\frac{4}{5}$

$5x+10y=8$

Eliminate fractions by multiplying 10 on both sides of the second equation:

$10*x+10*\frac{y}{2} =10*\frac{7}{10}$

$10x+5y=7$

Current system:

$5x+10y=8$

$10x+5y=7$

Multiply the second equation by 2:

$5x+10y=8$

$20x+10y=14$

Subtract the first equation from the second equation:

$(20x+10y)-(5x+10y)=14-8$

$20x+10y-5x-10y=6$

$(10y-10y)+20x-5x=6$

$0+15x=6$

$\boxed{x=\frac{2}{5} }$

Substitute the x value back to one of the equations to get the y value:

$x+\frac{y}{2} =\frac{7}{10}$

$(\frac{2}{5}) +\frac{y}{2} =\frac{7}{10}$

$(\frac{2}{5}) +\frac{y}{2}-\frac{2}{5} =\frac{7}{10}-\frac{2}{5}$

$\frac{y}{2} =\frac{3}{10}$

$\frac{y}{2}*2 =\frac{3}{10}*2$

$\boxed{y=\frac{3}{5} }$

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

The answer is x = 2/5, y = 3/5 or (2/5, 3/5)

First, in order to avoid fractional values during calculation, multiply both equations by 10 to simplify.

1. 10 (x/2 + y) = 10 (4/5) ⇒ 5x + 10y = 8
2. 10 (x + y/2) = 10 (7/10) ⇒ 10x + 5y = 7

Multiply the 1st equation by 10 and 2nd equation by 5.

    3. 10 (5x +  10y) = 10 (8) ⇒ 50x + 100y = 80

    4. 5 (10x + 5y) = 5 (7) ⇒ 50x + 25y = 35

Subtract : 3rd equation - 4th equation

• 50x + 100y - 50x - 25y = 80 - 35
• 75y = 45
• y = 3/5

Now, substitute for x in the 1st equation to find y.

• x/2 + 3/5 = 4/5
• x/2 = 1/5
• x = 2/5