math problem

Question

0.04x-0.01y=0.5

0.27x+0.13y=9.3

Answer 1

0.04x - 0.01y = 0.5                 eq1

0.27x + 0.13y = 9.3                eq2

 

Multiply eq1  by 0.13

 

0.0052x - 0.0013y = 0.065

 

Multiply eq2  by 0.01

 

0.0027x + 0.0013y = 0.093

 

Now we can add the two new equations to cancel out the y terms.  We obtain

 

0.0079x = 0.158

          x = 20

 

Substitute this value into eq2.

 

0.27x + 0.13y = 9.3

0.27(20) + 0.13y = 9.3

5.4 + 0.13y = 9.3

         0.13y = 3.9

               y = 30

 

Your solutions are

 

x = 20

y = 30

 

 

To check:

substituting these values into eq1 will result in 0.5

substituting these values into eq2 will result in 9.3

 

 

 

 

 

 

Answer 2

0.04x - 0.01y = 0.5
0.27x + 0.13y = 9.3

 

Multiply both sides of the first equation by 13, so you can eliminate the y terms:

0.52x - 0.13y = 6.5

0.27x + 0.13y = 9.3

 

Add the equations together:

.79x = 15.8

 

Divide both sides by .79

x = 20

 

Plug 20 in for x in one of the equations so you can solve for y:

0.04x - 0.01y = 0.5

0.04 * 20 - 0.01y = 0.5

.8 - .01y = .5

 

Subtract .8 from both sides:

-.01y = -.3

 

Divide both sides by -.01

y = 30

 

So x = 20 and y = 30.

 

You can plug these values into both of the original equations to check the results.