8q+6-2p=0
39=p-q
what is the solution or ordered pair
Rewrite
8q+6-2p=0
39=p-q
as
-2p + 8q = -6 ...(1)
p -q = 39 ...(2)
Eliminate p by adding 2*(2) to (1)
-2p + 8q + 2p -2q = -6 + 78
6q = 72
q = 12
Substitute q=12 in (2) to solve for p:
p - 12 = 39
p = 51
To find the solution or ordered pair, we can solve the system of equations:
1) 8q + 6 - 2p = 0
2) 39 = p - q
We can start by solving equation 2 for q and substituting it into equation 1.
From equation 2:
p = 39 + q
Now, substitute p = 39 + q into equation 1:
8q + 6 - 2(39 + q) = 0
Simplify the equation:
8q + 6 - 78 - 2q = 0
6q - 72 = 0
Add 72 to both sides:
6q = 72
q = 72/6
q = 12
Now substitute q = 12 into equation 2 to find the value of p:
39 = p - 12
Add 12 to both sides:
p = 39 + 12
p = 51
Therefore, the solution or ordered pair is (p, q) = (51, 12).
To find the solution or ordered pair for the given system of equations:
1. Start with the first equation:
8q + 6 - 2p = 0
2. Simplify the equation:
8q - 2p = -6
3. Now, move to the second equation:
39 = p - q
4. Rearrange the equation to isolate one of the variables:
p - q = 39
5. Now we have two equations:
8q - 2p = -6 - Equation 1
p - q = 39 - Equation 2
6. We can use either substitution or elimination method to solve the system of equations. Let's use the elimination method:
Multiply Equation 2 by 2 to eliminate the p term:
2(p - q) = 2(39)
2p - 2q = 78 - Equation 3
7. Subtract Equation 3 from Equation 1 to eliminate the p term:
(8q - 2p) - (2p - 2q) = (-6) - (78)
8q - 2p - 2p + 2q = -6 - 78
8q + 2q - 2p - 2p = -84
10q - 4p = -84
8. Simplify the equation:
10q - 4p = -84 - Equation 4
9. Now, we have a new equation 4:
10q - 4p = -84
10. Let's rewrite Equation 4 in terms of p:
-4p = -10q - 84
4p = 10q + 84
11. Divide both sides of the equation by 4:
p = (10q + 84)/4
p = 2.5q + 21
12. Now, we can substitute the expression for p in Equation 2:
p - q = 39
(2.5q + 21) - q = 39
13. Simplify the equation:
2.5q + 21 - q = 39
1.5q + 21 = 39
14. Subtract 21 from both sides of the equation:
1.5q = 39 - 21
1.5q = 18
15. Divide both sides of the equation by 1.5:
q = 18 / 1.5
q = 12
16. Now, substitute the value of q back into Equation 2 to find p:
p - q = 39
p - 12 = 39
17. Add 12 to both sides of the equation:
p = 39 + 12
p = 51
18. Thus, the solution or ordered pair for the system of equations is:
(p, q) = (51, 12)