Explain how you find ordered-pair solutions of the equation 3x – 5y = 15, and then find two such solutions.
To find ordered-pair solutions of the equation 3x - 5y = 15, you can use a method called substitution. Here are the steps:
Step 1: Choose a value for one of the variables. It can be any value you like. Let's choose x = 2 for the first solution.
Step 2: Substitute the chosen value into the equation and solve for the other variable.
3(2) - 5y = 15
6 - 5y = 15
-5y = 15 - 6
-5y = 9
y = 9/-5
y = -9/5
So the first solution is (2, -9/5).
Step 3: Repeat steps 1 and 2 to find another solution. Let's choose x = 5 this time.
Step 4: Substitute the chosen value into the equation and solve for the other variable.
3(5) - 5y = 15
15 - 5y = 15
-5y = 0
y = 0/-5
y = 0
So the second solution is (5, 0).
Therefore, the two ordered-pair solutions of the equation 3x - 5y = 15 are (2, -9/5) and (5, 0).
To find ordered-pair solutions of the equation 3x - 5y = 15, we need to substitute different values for x and y and see when the equation holds true.
1. Start by choosing a value for x. Let's say we pick x = 0 for the first solution.
- Substitute x = 0 into the equation: 3(0) - 5y = 15.
- Simplify: -5y = 15.
- Solve for y: y = -3.
- So, the first ordered-pair solution is (0, -3).
2. Now, choose a different value for x. Let's choose x = 5 for the second solution.
- Substitute x = 5 into the equation: 3(5) - 5y = 15.
- Simplify: 15 - 5y = 15.
- Solve for y: -5y = 0.
- Simplify further: y = 0.
- Therefore, the second ordered-pair solution is (5, 0).
So, the two ordered-pair solutions of the equation 3x - 5y = 15 are (0, -3) and (5, 0).