Solve Graphically the following simultaneous linear equations

2y-3x=12
x+6=y

Maths solve question

Good

To solve the given system of simultaneous linear equations graphically, we will plot the graphs of the two equations on the same coordinate axes.

First, let's rearrange the given equations in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Equation 1: 2y - 3x = 12
Rearranging, we get: 2y = 3x + 12
Dividing each term by 2, we get: y = (3/2)x + 6

Equation 2: x + 6 = y

Now, let's plot the graphs:

1. Equation 1: y = (3/2)x + 6
To plot this equation, start by plotting the y-intercept, which is 6. Then, use the slope (3/2) to find another point on the line. For example, if x = 0, y = 6. If x = 2, y = 9.
Plot these two points and draw a straight line passing through them.

2. Equation 2: x + 6 = y
To plot this equation, rewrite it as y = x + 6 and find points on the line. For example, if x = 0, y = 6. If x = 2, y = 8.
Plot these two points and draw a straight line passing through them.

Once both lines are plotted, find the point where the two lines intersect. This point represents the solution to the system of equations.

The graph should look like this:

|
7 | _
| | \
6 | | \
| | \___
5 | | \
| | \
4 | | \
| | \
3 | |________\
|
2--------------------------------
0 1 2 3 4 5 6

From the graph, we can see that the lines intersect at the point (4, 10).

Therefore, the solution to the system of simultaneous linear equations is x = 4 and y = 10.

To solve the given system of simultaneous linear equations graphically, we need to plot the graphs of both equations on the same coordinate plane and find the point of intersection.

Step 1: Rearrange the equations in the form y = mx + c.

The given equations are:
Equation 1: 2y - 3x = 12 or y = (3/2)x + 6
Equation 2: x + 6 = y or y = x + 6

Step 2: Plot the graphs.

Equation 1: y = (3/2)x + 6
To plot this, we start by marking the y-intercept, which in this case is 6. So, plot the point (0, 6). Then, apply the slope (the coefficient of x) which is 3/2 or 1.5. From the y-intercept point, move 3 units up and 2 units to the right (or down 3 units and 2 units to the left) and mark another point. Draw a straight line passing through these two points.

Equation 2: y = x + 6
To plot this, we start by marking the y-intercept, which in this case is 6. So, plot the point (0, 6). Then, use the slope of 1. From the y-intercept point, move 1 unit up and 1 unit to the right (or down 1 unit and 1 unit to the left) and mark another point. Draw a straight line passing through these two points.

Step 3: Find the point of intersection.

The point where the two lines intersect is the solution to the simultaneous equations. In this case, the lines intersect at the point (-6, 0). Therefore, the solution to the system of equations is x = -6 and y = 0.

So, the graphical solution to the given system of equations is x = -6 and y = 0.