Question

Is each ordered pair a solution of the inequality? $$2 x+5 y \geq 10 ;(1,2),(6,1)$$

Short answer

Both ordered pairs \((1,2)\) and \((6,1)\) are solutions to the inequality \(2x + 5y \geq 10\).

Step-by-step solution

Substitute the First Pair

Replace \(x\) and \(y\) in the inequality \(2x + 5y \geq 10\) with the values of the first pair, which is \((1, 2)\). According to substitution rule, this results in \(2(1) + 5(2) \geq 10\).

Check the First Pair

Calculate left side of the inequality to check if it's larger or equal to 10. The resulting calculation is 2 + 10 = 12. Since 12 is greater than 10, the inequality holds true. Therefore, \((1, 2)\) is a solution to the inequality.

Substitute the Second Pair

Replace \(x\) and \(y\) in the inequality \(2x + 5y \geq 10\) with the values of the second pair, which is \((6, 1)\). According to substitution rule, this results in \(2(6) + 5(1) \geq 10\).

Check the Second Pair

Calculate left side of the inequality to check if it's larger or equal to 10. The resulting calculation is 12 + 5 = 17. Since 17 is greater than 10, the inequality holds true. Therefore, \((6, 1)\) is also a solution to the inequality.