1. Finding the Missing Coordinate

2. 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:

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:

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

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.

6. 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!

7. 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)

8. 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)

9. 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.

10. 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

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

12. 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

13. 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

14. 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)