Find five solution sets for the linear equation 3x - 5y = 15.
pick any pairs (x,y) of values you want, as long as y = 3/5 x - 3
(0,-3)
(5,0)
...
There's only one solution set, however. It has infinitely many members, each obeying the rule 3x-5y=15.
To find solution sets for the linear equation 3x - 5y = 15, we need to assign values to either x or y and solve for the other variable. Let's solve for y in terms of x:
Step 1: Start with the equation 3x - 5y = 15.
Step 2: Subtract 3x from both sides to isolate the y term: -5y = -3x + 15.
Step 3: Divide both sides of the equation by -5 to solve for y: y = (3/5)x - 3.
Now we can assign values to x to find the corresponding values of y. Let's find five solution sets:
Solution set 1:
Let's let x = 0.
Substituting x = 0 into the equation y = (3/5)x - 3, we get:
y = (3/5)(0) - 3
y = -3.
So, the first solution set is (0, -3).
Solution set 2:
Let's let x = 5.
Substituting x = 5 into the equation y = (3/5)x - 3, we get:
y = (3/5)(5) - 3
y = 3 - 3
y = 0.
So, the second solution set is (5, 0).
Solution set 3:
Let's let x = -10.
Substituting x = -10 into the equation y = (3/5)x - 3, we get:
y = (3/5)(-10) - 3
y = -6 - 3
y = -9.
So, the third solution set is (-10, -9).
Solution set 4:
Let's let x = 2.
Substituting x = 2 into the equation y = (3/5)x - 3, we get:
y = (3/5)(2) - 3
y = 6/5 - 3
y = -9/5.
So, the fourth solution set is (2, -9/5).
Solution set 5:
Let's let x = -3.
Substituting x = -3 into the equation y = (3/5)x - 3, we get:
y = (3/5)(-3) - 3
y = -9/5 - 3
y = -24/5.
So, the fifth solution set is (-3, -24/5).
Therefore, the five solution sets for the linear equation 3x - 5y = 15 are:
(0, -3), (5, 0), (-10, -9), (2, -9/5), and (-3, -24/5).
To find solution sets for the linear equation 3x - 5y = 15, we need to find five different pairs of values for x and y that satisfy the equation.
Here's one way to find these solution sets:
1. Choose a value for x and solve for y:
Let's choose x = 1:
3(1) - 5y = 15
3 - 5y = 15
-5y = 12
y = -12/5
So, one solution set is x = 1, y = -12/5.
2. Choose another value for x and solve for y:
Let's choose x = 4:
3(4) - 5y = 15
12 - 5y = 15
-5y = 3
y = -3/5
The second solution set is x = 4, y = -3/5.
3. Choose another value for x and solve for y:
Let's choose x = 0:
3(0) - 5y = 15
-5y = 15
y = -15/5
y = -3
The third solution set is x = 0, y = -3.
4. Choose another value for x and solve for y:
Let's choose x = -2:
3(-2) - 5y = 15
-6 - 5y = 15
-5y = 21
y = -21/5
The fourth solution set is x = -2, y = -21/5.
5. Choose another value for x and solve for y:
Let's choose x = 5:
3(5) - 5y = 15
15 - 5y = 15
-5y = 0
y = 0
The fifth solution set is x = 5, y = 0.
Therefore, five solution sets for the linear equation 3x - 5y = 15 are:
1) (x = 1, y = -12/5)
2) (x = 4, y = -3/5)
3) (x = 0, y = -3)
4) (x = -2, y = -21/5)
5) (x = 5, y = 0)