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
this is way out there for us, she's only in 5th grade, but thank you
To solve the given system of equations:
1. Start with the two equations:
5x + 4y = 5 (Equation 1)
4x + 3y = 5 (Equation 2)
2. Multiply Equation 1 by 3 and Equation 2 by 4 to make the coefficients of 'y' the same:
15x + 12y = 15 (Multiplying Equation 1 by 3)
16x + 12y = 20 (Multiplying Equation 2 by 4)
3. Now, subtract Equation 1 from Equation 2 to eliminate 'y':
(16x + 12y) - (15x + 12y) = 20 - 15
Simplify:
x = 5
4. Substitute the value of 'x' (which is 5) into either of the original equations (let's use Equation 1):
5(5) + 4y = 5
25 + 4y = 5
Subtract 25 from both sides:
4y = -20
Divide both sides by 4:
y = -5
Therefore, the solution to the system of equations is x = 5 and y = -5.
However, it seems like there are additional equations provided after this point. Let's continue solving them:
5. The additional equations are:
15x + 12y = 18 (Equation 3)
20x + 16y = 24 (Equation 4)
6. Multiply Equation 3 by 5 and Equation 4 by 3 to make the coefficients of 'x' the same:
75x + 60y = 90 (Multiplying Equation 3 by 5)
60x + 48y = 72 (Multiplying Equation 4 by 3)
7. Subtract Equation 4 from Equation 3 to eliminate 'y':
(75x + 60y) - (60x + 48y) = 90 - 72
Simplify:
15x + 12y = 18
8. We can see that Equation 3 is the same as the third equation provided at the beginning. Hence, the value of x remains the same, which is x = 5.
9. Substituting x = 5 into Equation 3:
15(5) + 12y = 18
75 + 12y = 18
Subtract 75 from both sides:
12y = -57
Divide both sides by 12:
y = -57/12
Simplify the fraction:
y = -19/4
So, for Equation 3, we have x = 5 and y = -19/4.
10. For the last set of equations:
20x + 16y = 24 (Equation 5)
20x + 15y = 5 (Equation 6)
11. Subtract Equation 6 from Equation 5 to eliminate 'x':
(20x + 16y) - (20x + 15y) = 24 - 5
Simplify:
y = 19
Hence, the solution to Equation 5 and Equation 6 gives x = 5 and y = 19.
12. Finally, to find the sum of x and y:
x + y = 5 + 19
x + y = 24
Therefore, the sum of x and y is 24, or in mixed fraction format, it can be expressed as 2 5/31.