solve 4x-3y-6=0; x+3y-9=0 graphically
A graphical solution would be achieved by plotting both lines on an x-y graph and seeing where they interesect.
We lack the tools to do graphing for you.
By adding the two equations you can eliminate the y variable and see immediatley that
5x - 15 = 0
x = 3
Then use either of your equations for y.
12 - 3y = 6
3y = 6
y = 2
To solve the system of equations 4x - 3y - 6 = 0 and x + 3y - 9 = 0 graphically, we can plot the two equations on a graph and determine the coordinates of the intersection point.
Step 1: Rewrite the equations in slope-intercept form, y = mx + b.
Equation 1: 4x - 3y - 6 = 0
Rearrange to solve for y:
-3y = -4x + 6
Divide by -3:
y = (4/3)x - 2
Equation 2: x + 3y - 9 = 0
Rearrange to solve for y:
3y = -x + 9
Divide by 3:
y = -1/3x + 3
Step 2: Plot the lines on a graph.
Create a coordinate plane and label it. Choose a suitable scale on each axis to accurately plot the points.
For Equation 1, the slope (m) is 4/3 and the y-intercept (b) is -2. Plot the y-intercept at (0, -2) and use the slope to plot additional points. Draw a line through the points.
For Equation 2, the slope (m) is -1/3 and the y-intercept (b) is 3. Plot the y-intercept at (0, 3) and use the slope to plot additional points. Draw a line through the points.
Step 3: Find the intersection point.
The point where the two lines intersect is the solution to the system of equations. It represents the values of x and y that satisfy both equations simultaneously.
Locate the point where the two lines cross each other on the graph. Mark this point and find the coordinates.
Step 4: Read the solution.
Read the coordinates of the intersection point. The x-coordinate represents the value of x in the solution, and the y-coordinate represents the value of y in the solution.
This graphical method provides an approximate solution to the system of equations. In this case, it may not be possible to find the exact values of x and y without the use of additional methods such as substitution or elimination.