solve the system of equation!

Question

9x+10y=21

7x+11y=26

Answer 1

The easiest way of solving this is to eliminate one of the variables.  If you multiply each of the equations by a number so you can add the equations together and have only one variable left, you can solve the single variable equation.  Try multiplying the first equation by 11, the second by -10 and adding them, thus eliminating the y  variable.  After this, substitute that value you have for x and solve for y.  I hope this helps. 

Kevin

Answer 2

1. first solve for one of the variables in one of the equations

9x+10y=21 --->  9x=21-10y ---> x=21/9 - 10y/9

2. plug your newly modified equation into the second equation for x

7(21/9 - 10y/9) + 11y=26

3. now you can begin to solve for y

-first distribute the 7 to the fractions in parentheses (remember 7 is simply 7/1 so you will multiply the numerators together and the denominators together)

147/9 - 70y/9 + 11y = 26

4. Next try to simply your fractions.  This is easily done by seeing if the denominator or any of its factors goes into the numerator evenly (the factors of 9 are 1,3,9)

43/3 - 70y/9 +11y = 26  <--- for 43/3, three went into but the top and bottom

5. Now we will combine 70y/9 and 11y.  Again, remember that 11y = 11y/1 so we will match this denominator( 11y/1 ) with 70y/9 by multiplying the fraction by 9/9.

70y/9 + 99y/9 (then add the numerator and keep the denominator the same) ---> 169y/9

 

6. Now solve for y

43/3 - 169y/9 = 26    --->     -169y/9 = 26/1 - 43/3     --->     (169/9)y = 78/3 - 43/3

(169/9)y = 35/3    --->    y = (35/3) / (169/9)    --->   y = 35/5  x  9/169    --->   y = 315/845

simply the fraction by 5 ---> y = 63/169

7. now plug y back into the first equation and solve for x

9x + 10(63/169) = 21   ---> 9x + (630/169) =  21     --->    9x = 21 - (630/169)

x = (21/9) - (630/169)/(9/1)   --->   x= 21/9 - (630/169) x 1/9   ---> x= 21/9 - (630/1521)

x = (169/169) x 21/9 - (630/1521)   ---> x = 3549/1521  - 630/1521  ---> x = 2919/1521

x = 973/507  and  y = 63/169