Solve the system of equations by graphing then classify the system

4x+y=26
5x+6y=4

Graph the 2 Eqs. The point Of intersection is the solution.

Use the following points for graphing:

Eq1: 4X + Y = 26. (5, 6), (7, -2).

Eq2: 5X + 6Y = 4. (2, -1), (8, -6).

5. Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.

4x – 5y = -7
-8x + 10y = 14

To solve the system of equations by graphing, we can start by rearranging the equations to solve for y in terms of x.

First equation: 4x + y = 26
Rearrange to isolate y: y = 26 - 4x

Second equation: 5x + 6y = 4
Rearrange to isolate y: 6y = 4 - 5x
y = (4 - 5x) / 6

Now we have the equations in slope-intercept form (y = mx + b). We can graph the equations on the coordinate plane by choosing several values for x and calculating the corresponding values for y.

For the first equation (y = 26 - 4x):
When x = 0, y = 26 - 4(0) = 26
When x = 1, y = 26 - 4(1) = 22
When x = 2, y = 26 - 4(2) = 18

For the second equation (y = (4 - 5x) / 6):
When x = 0, y = (4 - 5(0)) / 6 = 4/6 = 2/3
When x = 1, y = (4 - 5(1)) / 6 = -1/6
When x = 2, y = (4 - 5(2)) / 6 = -6/6 = -1

Plotting the points (0, 26), (1, 22), (2, 18) for the first equation and (0, 2/3), (1, -1/6), (2, -1) for the second equation, we can now draw their graphs on the coordinate plane.

The graphs intersect at a single point, indicating that there is a unique solution to the system of equations. Therefore, the system is classified as consistent and independent.

To solve the system of equations by graphing, we will first need to graph each equation on the same coordinate plane. Then, we can observe where the two graphs intersect, as the coordinates of the intersection point will be the solution to the system.

Let's start by graphing the first equation, 4x + y = 26:

Step 1: Solve for y:
y = 26 - 4x

Step 2: Choose some x-values and find the corresponding y-values to plot points on the graph. For simplicity, let's choose three x-values and find their corresponding y-values:
When x = 0, y = 26 - 4(0) = 26
When x = 5, y = 26 - 4(5) = 6
When x = 10, y = 26 - 4(10) = -14

Step 3: Plot the points (0, 26), (5, 6), and (10, -14) on the graph, and connect them to form a straight line. This represents the graph of the first equation.

Now let's graph the second equation, 5x + 6y = 4:

Step 1: Solve for y:
6y = 4 - 5x
y = (4 - 5x)/6

Step 2: Choose some x-values and find the corresponding y-values to plot points on the graph. Let's use the same x-values as before:
When x = 0, y = (4 - 5(0))/6 = 4/6 = 2/3
When x = 5, y = (4 - 5(5))/6 = (4 - 25)/6 = -21/6 = -7/2
When x = 10, y = (4 - 5(10))/6 = (4 - 50)/6 = -46/6 = -23/3

Step 3: Plot the points (0, 2/3), (5, -7/2), and (10, -23/3) on the graph, and connect them to form a straight line. This represents the graph of the second equation.

Now, observe the graphed lines and look for the point where they intersect. The coordinates of that point represent the solution to the system of equations.

If the lines intersect at a single point, it means that the system has a unique solution, which means it is consistent and independent.

If the lines are parallel and do not intersect, it means that the system does not have a solution. In this case, it is inconsistent.

If the lines coincide and overlap, it means that the system has infinitely many solutions. This is the consistent and dependent case.

By examining the graph, you can determine the classification of the system based on the intersection point or if there is no intersection.