Question

solve the system of equations and give the value of x. ok, now for fractions..... x/7+y/21+1... x/2-y/6+0.... A. x=21/2... B.x=7/2 C. infintiely many solutions. D no solutions.

Answer 1

Your equations should be written as follows:
x/7 + y/21 = 1
x/2 - y/6 = 0
Yes???

Answer 2

@cralls18 Are you there?

Answer 3

yess sorry

Answer 4

yes you are correct... thats how its written

Answer 5

\[\frac{x}{7}+\frac{y}{21}=1...............(1)\]
\[\frac{x}{2}-\frac{y}{6}=0.............(2)\]
If you multiply both sides of (1) by 7 and multiply both sides of (2) by 2 you will find both of the modified equations begin with x (the x terms are no longer fractions). Can you do this step and post the results. Then I will explain the next step.

Answer 6

the denominators?

Answer 7

Multiply both sides of (1) by 7 as follows:
\[(7\times \frac{x}{7})+(7\times \frac{y}{21})=1\times 7\]
What do you get when you multiply it out?

Answer 8

\[7\times \frac{x}{7}=\frac{7x}{7}=?\]
\[7\times \frac{y}{21}=\frac{7y}{21}=?\]
\[1\times 7=?\]

Answer 9

i apologize, i stepped away for a minute... ok, fractions is my worse subject in math.... so would i multiply 7*7+x? or make 7 a common denominator with 21?

Answer 10

7x/7 =?

Answer 11

1

Answer 12

7/7 = 1
7x/7 = x
Do you follow?

Answer 13

yes

Answer 14

Good :) Then how about 7y/21 = ?
(Hint divide the numerator and then the denominator by 7).

Answer 15

3

Answer 16

1/3

Answer 17

7/21 = 1/3
7y/21 = y/3
Do you follow?

Answer 18

yes sir/ma'am?

Answer 19

Great! So now our equation (1) when both sides have been multiplied by 7 has become:
\[x+\frac{y}{3}=7..............(3)\]
And when we multiply both sides of equation (2) by 2 it becomes:
\[x-\frac{y}{3}=0.............(4)\]
The next step is to subtract equation (4) from equation (3). If we look at the x terms, we have x minus x = 0. Therefore we have eliminated x.
If we look at the y terms, we have y/3 minus (-y/3) = can you work this out?

Answer 20

y/0.. y--y would be +... 3-3=0.. right?

Answer 21

so the answer to the question is no solution?

Answer 22

or infinitely many solutions?

Answer 23

no it has solution

Answer 24

This problem does have a solution.
\[\frac{y}{3}-(-\frac{y}{3})=\frac{y+y}{3}=\frac{2y}{3}\]
Remembering that (a/b) - (-a/b) = (a + a)/b
+ * + = +
- * - = +
+ * - = -
- * + = -

Answer 25

So the result of subtracting (4) from (3) is as follows:
\[\frac{2y}{3}=7\]
\[y=\frac{21}{2}\]
If this value for y is substituted into (3) we get:
\[x+\frac{21}{2\times 3}=7\]
\[x=7-\frac{7}{2}=you\ can\ calculate\]

Answer 26

Choose 2 as a common denominator:
\[x=\frac{(7\times 2)-7}{2}=\frac{14-7}{2}=?\]