QuestionJune 7, 2025

Which ordered pair (p,r) is the solution to the given syst ) 5p-3r=1 8p+6r=4 (-1,-2) (-2,-1) ((2)/(9),(1)/(3)) ((1)/(3),(2)/(9))

Which ordered pair (p,r) is the solution to the given syst ) 5p-3r=1 8p+6r=4 (-1,-2) (-2,-1) ((2)/(9),(1)/(3)) ((1)/(3),(2)/(9))
Which ordered pair (p,r) is the solution to the given syst ) 5p-3r=1 8p+6r=4 (-1,-2) (-2,-1) ((2)/(9),(1)/(3)) ((1)/(3),(2)/(9))

Solution
4.7(212 votes)

Answer

\left(\frac{1}{3}, \frac{2}{9}\right) Explanation 1. Substitute the first pair into equations For (-1, -2): 5(-1) - 3(-2) = -5 + 6 = 1; 8(-1) + 6(-2) = -8 - 12 = -20 \neq 4. Not a solution. 2. Substitute the second pair into equations For (-2, -1): 5(-2) - 3(-1) = -10 + 3 = -7 \neq 1; 8(-2) + 6(-1) = -16 - 6 = -22 \neq 4. Not a solution. 3. Substitute the third pair into equations For \left(\frac{2}{9}, \frac{1}{3}\right): 5\left(\frac{2}{9}\right) - 3\left(\frac{1}{3}\right) = \frac{10}{9} - 1 = \frac{1}{9} \neq 1; 8\left(\frac{2}{9}\right) + 6\left(\frac{1}{3}\right) = \frac{16}{9} + 2 = \frac{34}{9} \neq 4. Not a solution. 4. Substitute the fourth pair into equations For \left(\frac{1}{3}, \frac{2}{9}\right): 5\left(\frac{1}{3}\right) - 3\left(\frac{2}{9}\right) = \frac{5}{3} - \frac{2}{3} = 1; 8\left(\frac{1}{3}\right) + 6\left(\frac{2}{9}\right) = \frac{8}{3} + \frac{4}{3} = 4. Both equations are satisfied.

Explanation

1. Substitute the first pair into equations<br /> For $(-1, -2)$: $5(-1) - 3(-2) = -5 + 6 = 1$; $8(-1) + 6(-2) = -8 - 12 = -20 \neq 4$. Not a solution.<br />2. Substitute the second pair into equations<br /> For $(-2, -1)$: $5(-2) - 3(-1) = -10 + 3 = -7 \neq 1$; $8(-2) + 6(-1) = -16 - 6 = -22 \neq 4$. Not a solution.<br />3. Substitute the third pair into equations<br /> For $\left(\frac{2}{9}, \frac{1}{3}\right)$: $5\left(\frac{2}{9}\right) - 3\left(\frac{1}{3}\right) = \frac{10}{9} - 1 = \frac{1}{9} \neq 1$; $8\left(\frac{2}{9}\right) + 6\left(\frac{1}{3}\right) = \frac{16}{9} + 2 = \frac{34}{9} \neq 4$. Not a solution.<br />4. Substitute the fourth pair into equations<br /> For $\left(\frac{1}{3}, \frac{2}{9}\right)$: $5\left(\frac{1}{3}\right) - 3\left(\frac{2}{9}\right) = \frac{5}{3} - \frac{2}{3} = 1$; $8\left(\frac{1}{3}\right) + 6\left(\frac{2}{9}\right) = \frac{8}{3} + \frac{4}{3} = 4$. Both equations are satisfied.
Click to rate:

Similar Questions