Solve the system by using a table.
-0.6x - 0.6y = -0.6
0.5x - 0.3y = -2.7
To solve this system using a table, we will create a table with three columns for x, y, and the equations.
----------------------------------
| x | y | -0.6x - 0.6y = -0.6 |
----------------------------------
| | | 0.5x - 0.3y = -2.7 |
----------------------------------
Next, we will choose values for x and find the corresponding values of y using the two equations.
Let's start with x = 0:
-----------------------------------
| 0 | y | -0.6(0) - 0.6y = -0.6 |
-----------------------------------
| | | 0.5(0) - 0.3y = -2.7 |
-----------------------------------
Simplifying the equations:
-0.6y = -0.6
-0.3y = -2.7
Solving for y:
-0.6y = -0.6
y = 1
-0.3y = -2.7
y = 9
Now let's check another value of x, x = 1:
-----------------------------------
| 1 | y | -0.6(1) - 0.6y = -0.6 |
-----------------------------------
| | | 0.5(1) - 0.3y = -2.7 |
-----------------------------------
Simplifying the equations:
-0.6 - 0.6y = -0.6
0.5 - 0.3y = -2.7
Solving for y:
-0.6 - 0.6y = -0.6
-0.6y = 0
y = 0
0.5 - 0.3y = -2.7
-0.3y = -3.2
y = 10.67 or approximately 10.7
Now we have two values for y for each value of x. We can write the solutions as (0, 1) and (1, 10.7).
To solve the system using a table, we can use a table to organize our work and find the values of x and y that satisfy both equations.
We'll start by creating a table with two columns for x and y.
```
| x | y |
|-------|-------|
| | |
```
Now, let's substitute some arbitrary values for x and calculate the corresponding value of y for each equation.
Let's choose x = 0 for simplicity.
When x = 0, the first equation becomes:
-0.6(0) - 0.6y = -0.6
-0.6y = -0.6
Divide both sides by -0.6:
y = 1
So when x = 0, y = 1 for the first equation.
Now, let's substitute x = 0 into the second equation:
0.5(0) - 0.3y = -2.7
-0.3y = -2.7
Divide by -0.3:
y = 9
Therefore, when x = 0, y = 9 for the second equation.
Now, we can fill in our table with the values we found:
```
| x | y |
|-------|-------|
| 0 | 1 |
| 0 | 9 |
```
Since x = 0 and y = 1 satisfy the first equation, and x = 0 and y = 9 satisfy the second equation, the solution to the system of equations is x = 0 and y = 1 (or x = 0 and y = 9).
To solve the given system of equations using a table, we will create a table and substitute values for one variable, typically x or y, in both equations to find the corresponding values for the other variable. Here's how you can do it step by step:
Step 1: Create the table with two columns, one for x and one for y.
Step 2: Choose a value for x and substitute it into the first equation -0.6x - 0.6y = -0.6. Solve the equation for y.
Step 3: Repeat step 2, but substitute the same value for x into the second equation 0.5x - 0.3y = -2.7. Solve the equation for y.
Step 4: Record the calculated values of x and y in the table.
Step 5: Repeat steps 2-4 with different values of x until you have at least two ordered pairs (x, y) for the system.
Step 6: Check if the ordered pairs obtained satisfy both equations of the system. If they do, the ordered pair is a solution to the system.
Let's solve the given system using a table:
Step 1: Create the table.
x | y
----------------
|
|
|
Step 2: Assume a value for x, let's choose x = 0.
x | y
----------------
0 |
|
|
Step 3: Substitute x = 0 into the first equation:
-0.6(0) - 0.6y = -0.6
-0 - 0.6y = -0.6
-0.6y = -0.6
y = -0.6 / -0.6
y = 1
Now substitute x = 0 into the second equation:
0.5(0) - 0.3y = -2.7
0 - 0.3y = -2.7
-0.3y = -2.7
y = -2.7 / -0.3
y = 9
Step 4: Record the values of x and y in the table.
x | y
----------------
0 | 1
|
|
Step 5: Choose a different value for x. Let's choose x = 1.
x | y
----------------
0 | 1
1 |
|
Step 6: Substitute x = 1 into the first equation:
-0.6(1) - 0.6y = -0.6
-0.6 - 0.6y = -0.6
-0.6y = -0.6 + 0.6
-0.6y = 0
y = 0 / -0.6
y = 0
Now substitute x = 1 into the second equation:
0.5(1) - 0.3y = -2.7
0.5 - 0.3y = -2.7
-0.3y = -2.7 - 0.5
-0.3y = -3.2
y = -3.2 / -0.3
y ≈ 10.67
Step 7: Record the values of x and y in the table.
x | y
----------------
0 | 1
1 | 10.67
|
Step 8: Check if the ordered pairs (x, y) satisfy both equations.
When x = 0 and y = 1, substitute these values into both equations:
-0.6x - 0.6y = -0.6
-0.6(0) - 0.6(1) = -0.6
0 - 0.6 = -0.6
-0.6 = -0.6 (satisfied)
0.5x - 0.3y = -2.7
0.5(0) - 0.3(1) = -2.7
0 - 0.3 = -2.7
-0.3 = -2.7 (satisfied)
Both equations are satisfied, so the ordered pair (x, y) = (0, 1) is a solution to the system.
Similarly, when x = 1 and y ≈ 10.67, substitute these values into both equations:
-0.6x - 0.6y = -0.6
-0.6(1) - 0.6(10.67) = -0.6
-0.6 - 6.402 = -0.6
-7.002 ≈ -0.6 (not satisfied)
0.5x - 0.3y = -2.7
0.5(1) - 0.3(10.67) = -2.7
0.5 - 3.201 = -2.7
-2.701 = -2.7 (satisfied)
The second equation is satisfied, but the first equation is not satisfied. Therefore, the ordered pair (x, y) = (1, 10.67) is not a solution to the system.
In conclusion, the only solution to the given system of equations is (x, y) = (0, 1).