Respuesta :
The answer to this question is
2r+3p=15.50
Now use equation (1) with equation 2 or equation 3 to eliminate A
2r+3p=15.50
Now use equation (1) with equation 2 or equation 3 to eliminate A
The values of a, r, and p are 7, 4, and 2.50 respectively, for the given system of equations as per linear equation.
What is a linear equation?
"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. "
Given, 2a + 3r + 1.5p = 29.75 (1)
a + r + p = 13.50 (2)
a + 3r + 4p= 29.00 (3)
Now, multiplying equation (2) by -1 and adding it to equation (3) we get:
(- a - r - p + a + 3r + 4p) = - 13.50 + 29.00
⇒ (2r + 3p) = 15.50 (4)
Now, multiplying equation (2) by 2 and subtracting from equation (1), we get:
(2a + 3r + 1.5p - 2a - 2r - 2p) = 29.75 - 27.00
⇒ (r - 0.5p) = 2.75 (5)
Again, multiplying equation (5) by 6 and adding with equation (4), we get:
(2r + 3p + 6r - 3p) = 15.50 + 16.50
⇒ 8r = 32.00
⇒ r = 4.00
Now substituting the value of 'r' in equation (5), we get:
4 - 0.5p = 2.75
⇒ - 0.5p = - 1.25
⇒ p = 2.50
Now, substituting the value of 'p' and 'r' in the equation (2), we get:
a + 4 + 2.50 = 13.50
⇒ a = 13.50 - 4.00 - 2.50
⇒ a = 7
Therefore, the values of a = 7, r = 4, p = 2.50.
Learn more about linear equation here: https://brainly.com/question/13591596
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