Which ordered pairs are solutions to the equation

Question

Which ordered pairs are solutions to the equation 6x+5y=5?

(2,−75), (3,−135), (0,1), (7,5)

Answer 1

Hi Anulika

Since you’ve listed Alegbra 2 above, can one assume that you are familiar with Slope intercept form for a line from Algebra 1?

Slope Intercept Form for a line is

y = mx + b

You can put your equation into this form by solving for y

6x + 5y = 5

y =(-6/5)x + 1

With this format, when x = 0 y = 1 so without calculation the ordered pair (0,1) makes the equation true.

Also in the pairs where x is not 5 or a multiple of 5 your answer or y value would be a fraction(improper fraction).

Finally, you can graph your line on a graphing calculator or at desmos.com to see if any of the giving points are on your line.

I hope this helps.

Answer 2

In this situation, only plugging in the values and checking to see if the equation holds will work.

Ordinarily, you need 2 equations in 2 unknowns to solve for an answer. But in this case, you only have one equation.

You could solve for 1 of the variables, plug in any value for one of the variables , and then use your revised equation to calculate the other variable. But there are an infinite number of solutions: in fact, every point on the given line.

This substitute-and-check method often works on multiple choice tests. However, test makers have developed methods to foil that technique, such as providing the sum or the product of the answers.

Answer 3

Hi Anulika,

Plug in each ordered pair for x and y in your equation and check if resulting statement is true:

6(2) + 5 (-75) = 5 No good

6(3) + 5(-135) = 5 No good

6(0)+ 5(1) = 5 Yes

6(7) + 5(5) = 5 No good

So, the only solution is the ordered pair (0,1). I hope this helps.