Question

When13p + 10q=25 and 2p + 5q= 17, what is the value of p

Answer 1

The value of p is -0.5, or
`(-1)/(2)`.

To find the value of p, we must isolate the variable. We can do so with the second equation:

2p + 5q = 17

⇒ 2p = 17 - 5q

⇒ p = (17 - 5q) ÷ 2

Next, we can substitute the value of p into the first equation:

13p + 10q = 25

⇒ 13(17 - 5q) ÷ 2 + 10q = 25

Then, we simplify:

(221 - 65q) ÷ 2 + 10q = 25

Now we multiply both sides of the equation by 2 to terminate the fraction:

221 - 65q + 20q = 50

Here, we combine like terms:

50 - 221 = -171

-65q + 20q = -45q

-45q = -171

Next, we divide by -45 to get the value that will be substituted to find p:

-171 ÷ (-45) = 3.8

So, q = 3.8.

Finally, we substitute q into the equation to find p:

p = (17 - 5(3.8)) ÷ 2

p = 17 - 19 ÷ 2

p = -1 ÷ 2

p = -0.5

When 13p + 10q = 25 and 2p + 5q = 17, the value of p is -0.5.