solve the system of equation by graphing ( find out where they meet.
x+3y=4
2x-y=8
so graph them. What is the question?
where do the two lines meet?
at what point on the graph do the two lines meet? e.g (x,Y)
To solve this system of equations by graphing, we will plot the lines represented by the equations and find the point where they intersect. This intersection point represents the solution to the system.
First, let's rewrite the equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
Equation 1:
x + 3y = 4 --> 3y = -x + 4 --> y = (-1/3)x + 4/3
Equation 2:
2x - y = 8 --> -y = -2x + 8 --> y = 2x - 8
Now, let's plot these lines on a graph:
Take a range of values for x (let's say -5 to 5) and substitute them into each equation to find the corresponding y values. Plot these points on a graph.
For Equation 1 (y = (-1/3)x + 4/3):
For x = -5, y = (-1/3)(-5) + 4/3 = 19/3
For x = -4, y = (-1/3)(-4) + 4/3 = 16/3
For x = -3, y = (-1/3)(-3) + 4/3 = 13/3
For x = -2, y = (-1/3)(-2) + 4/3 = 10/3
For x = -1, y = (-1/3)(-1) + 4/3 = 7/3
For x = 0, y = (-1/3)(0) + 4/3 = 4/3
For x = 1, y = (-1/3)(1) + 4/3 = 1/3
For x = 2, y = (-1/3)(2) + 4/3 = -2/3
For x = 3, y = (-1/3)(3) + 4/3 = -5/3
For x = 4, y = (-1/3)(4) + 4/3 = -8/3
For x = 5, y = (-1/3)(5) + 4/3 = -11/3
For Equation 2 (y = 2x - 8):
For x = -5, y = 2(-5) - 8 = -18
For x = -4, y = 2(-4) - 8 = -16
For x = -3, y = 2(-3) - 8 = -14
For x = -2, y = 2(-2) - 8 = -12
For x = -1, y = 2(-1) - 8 = -10
For x = 0, y = 2(0) - 8 = -8
For x = 1, y = 2(1) - 8 = -6
For x = 2, y = 2(2) - 8 = -4
For x = 3, y = 2(3) - 8 = -2
For x = 4, y = 2(4) - 8 = 0
For x = 5, y = 2(5) - 8 = 2
Plot these points on the graph. The line for Equation 1 will have a negative slope, and the line for Equation 2 will have a positive slope.
After plotting the points, you will see that the lines intersect at the point (3, -2). Therefore, the solution to the system of equations is x = 3 and y = -2.
Graphing the system of equations helps visualize the solution by finding the point of intersection. However, this method is not always accurate, especially if the lines intersect at a fraction or decimal value. In such cases, it is better to use algebraic methods like substitution or elimination to find the exact solution.