Finding the Missing Coordinate

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Presentation transcript:

Finding the Missing Coordinate

Solutions to equations If we have a simple equation like 4x + 6 = 18, the solution to that equation would be the value(s) of x that make it a true statement. Let’s try x = 3:

Solutions to equations If we have an equation like x + y = 6 we would need both a value for x and a value for y. Let’s try x = 2 and y = 4:

Solutions to equations Notice that there are other solutions to this equation as well. Let’s try x = 1 and y = 5:

Solutions to equations If you plotted all of the pairs of x and y that work in this equation and connected the dots, you would have a line.

Testing an ordered pair Sometimes they ask you if a given ordered pair is a solution to an equation. Remember that an ordered pair is always (x, y). Is (– 2, 5) a solution to 3x + 4y = 17? That’s like asking if x = – 2 and y = 5 will work in 3x + 4y = 17? NOT!

Complete the Ordered Pair Complete the ordered pair so that (5, ) is a solution to 2x + 3y = 16. That’s like asking you to find a value of y that will work in 2x + 3y = 16 if x = 5. The answer is (5, 2)

Finding the missing coordinate Complete the ordered pair so that ( , – 3) is a solution to 2x – 3y = 7. That’s like asking you to find a value of x that will work in 2x – 3y = 7 if y = – 3. The answer is (-1, -3)

Read the question carefully! If they ask you to complete the ordered pair, your answer will be an ordered pair in the format ( 2 , – 3) . If they ask you to find a value of a so that (a, – 3) is a solution to 2x – 3y = 7 the answer will be a number.

Do it yourself! What if they give you an equation and ask you to come up with three ordered pairs that work? Let’s find three solutions for the equation y = 2x + 3

Do it yourself! To find 3 ordered pair solution to the equation: y = 2x + 3 We will construct a table of values. x y

Pick values for the complicated side – the one with all the action! y = 2x + 3 Pick values for the complicated side – the one with all the action! In this example, pick 3 values for x. If you pick an ‘x’ that makes ‘y’ a fraction, pick again! x y

Pick small numbers so that the math will be easy! y = 2x + 3 Pick small numbers so that the math will be easy! 1 2 x y

Now figure out the corresponding y values! y = 2x + 3 Now figure out the corresponding y values! x y 2(0) + 3 = 3 (0, 3) 1 2(1) + 3 = 5 (1, 5) 2 2(2) + 3 = 7 (2, 7)