Hey guys, I have some difficulty with my math questions.
One of them is this:
In the following statement, there are two unknowns, x and y.
Write two equations and solve them.
1. The sum of two numbers is 21 and the difference is 7.
I came up with
x+y=21
x-y=7
is it right? If it is, I dont know how to go any further than that! Please help! thanks
Yeah!
(x+y=21) - (x-y=7)
= 2y=14
(/2) y=7
(x+7=21) so x=14
x=14 y=7
x + y = 21_________(1)
x - y = 7__________(2)
from equation (1); x = 21 - y________(3)
substitute equation (3) into equation (2);
21 - y - y = 7
21 - 2y = 7
-2y = 7 - 21
-2y = -14
2y = 14
y = 7
substitute y = 7 into equation (3);
x = 21 - 7
x = 14
You started off very well. To make things easier for yourself and for the marker, you should explain these statements also! :)
So:
Firstly, let the first number be represented by x, the second by y.
Equation 1: x+y = 21
Equation 2: x-y = 7
Add equations 1 and 2 together to obtain equation 3. (You do this as it will eliminate the second unknown, the y)
Equation 3: (x+y) + (x-y) = 21+7, [The y will now be cancelled out]
2x = 28
Hence x = 14
Now we can substitute x = 14 into any of the equations above to get the solution to y. Say we substitue x = 14 into equation 1:
14 + y = 21
Hence y = 7
The unknown digits are therefore 7 and 14.
Remember that usually at least x statements or pieces of information are needed to find out the answer to x unknowns. In this case, 2 pieces of information initially (Equations 1 and 2) were given and these could be used to solve for the two digits. Hope that helps! :)
You have set up the equations correctly. Next add the equations giving you 2x = 28>>> so x = 14. Next substitute x = 14 into either of the original equations and solve for y, y = 7. Finally, substitute x = 14 and y = 7 into each equation to check that each equation is a true statement.
Your two equations relate the variables as described. Suppose you were to solve the second equation for x (in terms of y). Would you get:
x = y + 7 ?
Then, substitute that expression for x in your first equation. So,
(y + 7) + y = 21
You can solve that, right ?!
Does that enable you to get a value for y, then x ? You can check by evaluating both equations.
Go for it.
x + y = 21 (solve by using substitution)
x - y = 7
x + y = 21
x = 21 - y
x - y = 7
(21 - y) - y = 7
21 - y - y = 7
-2y = 7 - 21
-2y = 14
y = -14/-2
y = 7
x + y = 21
x + 7 = 21
x = 21 - 7
x = 14
∴ x = 14 , y = 7
x + y = 21
x - y = 7
Rearrange the second equation.
x = y + 7
Substitute it in to the first equation.
( y + 7 ) + y = 21
= 2y + 7 = 21
= 2y = 14
Therefore y = 7.
Put this into one of the equations to find x.
x = y + 7
x = 7 + 7
x = 14
So y = 7
and
x = 14
Hope this helped :)
x + y = 21
x - y = 7
x + y = 21
+ x - y = 7
= 2x = 28
= x = 14
14 + y = 21
y = 7
therefore: x = 14, y = 7
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