Solving by substitution?

Question

What is the value of x and y when solved by substition?

1/x + 1/y = 3/4

3/x - 1/y = 1/4

and

2/x - 2/y = 1/2

1/x + 5/y = 3/4

Answer 1

Hi,

1/x + 1/y = 3/4

3/x - 1/y = 1/4

Add these equations and solve for x.

1/x + 1/y = 3/4

3/x - 1/y = 1/4

-----------------------

4/x = 1

4 = x

If x = 4, then:

1/4 + 1/y = 3/4

1/y = 1/2

y = 2

x = 4 and y = 2 <==ANSWER

and

2/x - 2/y = 1/2

1/x + 5/y = 3/4

Multiply first equation by 5 and second equation by 2. Add equations and solve for x.

5(2/x - 2/y = 1/2)

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

10/x - 10/y = 5/2

2/x + 10/y = 3/2

--------------------------

12/x = 4

12 = 4x

x = 3

If x = 3 then:

2/x - 2/y = 1/2

2/3 - 2/y = 1/2

-2/y = -1/6

y = 12

x = 3 and y = 12 <==ANSWER

I hope that helps!! :-)

Answer 2

Do you have to solve by substitution ?  It would be much easier to add the equations together.

1/x + 1/y = 3/4

3/x - 1/y = 1/4

-------------------------- Add straight down

4/x = 1

Cross multiply

x = 4

substitute...from first equation

1/4 + 1/y = 3/4

1/y = 2/4

y = 2 so the solution to the first one is (4, 2)

Problem 2 :  I would multiply the second equation by -2, then add straight down again, etc.

Good luck to you !

Answer 3

For these questions, it's easier to solve for 1/x and 1/y first:

1/y = 3/4 - 1/x

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

=> 4/x = 1

=> x = 4

=> y = 2

Use the same idea for the second set of equations.

Answer 4

for the first set  x=4  y=2

for second set   y=12  x=3