If 5x +4y and 4x +3y =5
15x +12y =18
16x +12y = 20
31x/31= 38/31
x= 1 7/31
20x +16y =24
20x +15y = 5
31/y/31 = 29/31
y=29/31
x +y = 1 7/31 + 29/31
2 5/31
No, both the x and y values are incorrect.
Notice in your elimination method, you forgot to multiply one of the equations by -1 so that when added will cancel the variable y. This one:
15x + 12y = 18
16x + 12y = 20
should be:
15x + 12y = 18
-16x - 12y = -20
so that when added, it becomes:
-x = -2
x = 2
Now, try solving y.
Hope this helps~ `u`
You apparently multiplied the first equation by 3 and the 2nd by 4.
Your first should have been
15x + 12y = 15 and then
16x + 12y = 20
subtract them
x = 5
back into the first:
5x+4y=5
25+4y=5
4y = -20
y = -5
your line of 31x/31= 38/31
makes no sense.
Looks like you added the two equations, one of which was wrong, but subracted the y's
Jai's answer is the correct one for what I think your problem actually was. X = 2 and Y = (-1).
When you wrote out the question originally, you or your Grandma didn't complete the first equation (should have been 5x + 4y = 6 (forgot the " = 6" part)) which made it kind of confusing, as if both equations = 5.
If you DID mean to say that both of the original equations = 5, then what Anonymous wrote is correct.
To solve the system of equations:
1) Start with the given equations:
5x + 4y = 5 (Equation 1)
4x + 3y = 5 (Equation 2)
2) Multiply Equation 1 by 3 and Equation 2 by 4 to eliminate the y term:
15x + 12y = 15 (Equation 3)
16x + 12y = 20 (Equation 4)
3) Subtract Equation 3 from Equation 4 to eliminate the y term:
(16x + 12y) - (15x + 12y) = 20 - 15
x = 5
4) Substitute x = 5 into Equation 1:
5(5) + 4y = 5
25 + 4y = 5
4y = 5 - 25
4y = -20
y = -20/4
y = -5
5) Therefore, the solution to the system of equations is x = 5 and y = -5.
Now, let's move on to the next set of equations:
1) Start with the given equations:
20x + 16y = 24 (Equation 5)
20x + 15y = 5 (Equation 6)
2) Multiply Equation 6 by 16 and Equation 5 by 15 to eliminate the x term:
320x + 240y = 80 (Equation 7)
300x + 240y = 360 (Equation 8)
3) Subtract Equation 7 from Equation 8 to eliminate the y term:
(300x + 240y) - (320x + 240y) = 360 - 80
-20x = 280
x = 280/-20
x = -14
4) Substitute x = -14 into Equation 5:
20(-14) + 16y = 24
-280 + 16y = 24
16y = 24 + 280
16y = 304
y = 304/16
y = 19
5) Therefore, the solution to the second set of equations is x = -14 and y = 19.
Finally, let's find the sum of x and y:
x + y = 5 + (-5) (from the first set of equations)
= -14 + 19 (from the second set of equations)
= -9
So, x + y = -9, which can be represented as a mixed number as 2 5/31.