an equation and two ordered pairs are given. show that each pair is a solution of the equation. Then graph the two pairs to determine another solution. 6x-3y=3; (1,1), (-1, -3)

6(1) -3(1) = 3 sure enough

6(-1) -3 (-3) = -6+3 = -3 No it is not.

Typo?

To show that each ordered pair is a solution of the equation 6x - 3y = 3, we can substitute the x and y values of each pair into the equation and verify that the equation is satisfied.

For the first ordered pair (1, 1):
Substituting x = 1 and y = 1 into the equation, we have:
6(1) - 3(1) = 3.
Simplifying, we get:
6 - 3 = 3,
3 = 3.
Since the equation is true, the pair (1, 1) is a solution to the equation.

For the second ordered pair (-1, -3):
Using the same process, substitute x = -1 and y = -3 into the equation:
6(-1) - 3(-3) = 3.
Simplifying, we have:
-6 + 9 = 3,
3 = 3.
Since the equation is true, the pair (-1, -3) is also a solution to the equation.

To graph the two pairs (1, 1) and (-1, -3) and determine another solution, we can plot these points on a coordinate plane and see where their corresponding line intersects another point.

Plotting (1, 1) and (-1, -3) on a graph:

| (1, 1)
|
------|------
|
| (-1, -3)

Now, let's find another point of intersection by drawing a straight line through the two plotted points. Extend the line in both directions:

| (1, 1)
|
------|------
|
| (-1, -3)
|
|
| (0, 0) <-- new point of intersection

We can estimate that the line passes through the point (0, 0). Hence, (0, 0) is another solution to the equation 6x - 3y = 3.

Therefore, the given equation is satisfied by each of the ordered pairs (1, 1) and (-1, -3). The graph also indicates that (0, 0) is another solution.

To show that each pair is a solution of the equation 6x - 3y = 3, we substitute the values of x and y from each ordered pair into the equation and check if the equation is satisfied.

1. First, let's check if (1, 1) is a solution:
Substitute x = 1 and y = 1 into the equation:
6(1) - 3(1) = 3
6 - 3 = 3
3 = 3

Since both sides of the equation are equal, the ordered pair (1, 1) is indeed a solution.

2. Now let's check if (-1, -3) is a solution:
Substitute x = -1 and y = -3 into the equation:
6(-1) - 3(-3) = 3
-6 + 9 = 3
3 = 3

Again, both sides of the equation are equal, so the ordered pair (-1, -3) satisfies the equation as well.

Therefore, both (1, 1) and (-1, -3) are solutions of the equation 6x - 3y = 3.

To graph the two pairs and find another solution, we can plot the points (1, 1) and (-1, -3) on a coordinate plane and extend the line to see where it intersects the y-axis.

Here's how to graph the points:
- Plot the point (1, 1) by moving right 1 unit along the x-axis and up 1 unit along the y-axis.
- Plot the point (-1, -3) by moving left 1 unit along the x-axis and down 3 units along the y-axis.

Now draw a line through these two points.

To find another solution, we need to determine the coordinates of the point where the line intersects the y-axis. This point will have an x-coordinate of 0.

We can find the y-coordinate by substituting x = 0 into the equation and solving for y:
6(0) - 3y = 3
0 - 3y = 3
-3y = 3
y = -1

Therefore, the point of intersection with the y-axis is (0, -1).

So, another solution to the equation 6x - 3y = 3 is (0, -1).

To summarize, the solutions to the equation 6x - 3y = 3 are (1, 1), (-1, -3), and (0, -1).