Solve this system of linear equations by graphing 2x-y=4 , 2x-y=6
Those two equations are parallel lines. There is no solution, since they do not intersect.
2x -y cannot be both 4 and 6.
To solve the system of linear equations by graphing, you need to graph each equation on the same coordinate plane and find the point where the two lines intersect. This point represents the solution to the system of equations.
First, let's rewrite the given equations in slope-intercept form (y = mx + b), where m represents the slope and b is the y-intercept.
1) 2x - y = 4:
-> -y = -2x + 4
-> y = 2x - 4
2) 2x - y = 6:
-> -y = -2x + 6
-> y = 2x - 6
Let's start graphing:
For equation 1), y = 2x - 4:
Choose some x-values, substitute them into the equation, and find the corresponding y-values.
For x = 0, y = 2(0) - 4 = -4. So, one point on the graph is (0, -4).
For x = 1, y = 2(1) - 4 = -2. So, another point on the graph is (1, -2).
Plot these two points and draw a line passing through them.
For equation 2), y = 2x - 6:
Choose some x-values, substitute them into the equation, and find the corresponding y-values.
For x = 0, y = 2(0) - 6 = -6. So, one point on the graph is (0, -6).
For x = 1, y = 2(1) - 6 = -4. So, another point on the graph is (1, -4).
Plot these two points and draw a line passing through them.
Now, look at the graph. The intersection point of the two lines is the solution to the system of equations. If there is no intersection, it means the system of equations has no solution.
In this case, by observing the graph, we can see that the two lines are parallel and do not intersect. Therefore, there is no solution for this system of linear equations.
Note: Graphing is a visual method to determine solutions to linear equations. However, for a more accurate and precise solution, you may consider using algebraic methods such as substitution or elimination.
To solve this system of linear equations by graphing, we will plot the lines represented by each equation on a coordinate plane and find their point of intersection. The point of intersection will be the solution to the system.
First, let's solve the first equation, 2x - y = 4, for y in terms of x:
- Subtract 2x from both sides: -y = -2x + 4
- Multiply both sides by -1 to isolate y: y = 2x - 4
Now, let's solve the second equation, 2x - y = 6, for y in terms of x:
- Subtract 2x from both sides: -y = -2x + 6
- Multiply both sides by -1 to isolate y: y = 2x - 6
Now we have two equations in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
To graph these equations, we can start by plotting two points on each line and then connecting them with a straight line.
For the equation y = 2x - 4:
- Choose two different x-values (e.g., -2 and 2) and substitute them into the equation to find the corresponding y-values:
- For x = -2: y = 2(-2) - 4 = -8
- For x = 2: y = 2(2) - 4 = 0
- Plot the points (-2, -8) and (2, 0) on the coordinate plane and draw a line passing through them.
For the equation y = 2x - 6:
- Choose two different x-values (e.g., -2 and 3) and substitute them into the equation to find the corresponding y-values:
- For x = -2: y = 2(-2) - 6 = -10
- For x = 3: y = 2(3) - 6 = 0
- Plot the points (-2, -10) and (3, 0) on the coordinate plane and draw a line passing through them.
Now, look at the graph and determine the point of intersection of the two lines. This point will be the solution to the system of equations.
If the lines are parallel and do not intersect, it means that the system has no solution.
If the two lines coincide and overlap, it means that the system has infinitely many solutions.
By following these steps, you should be able to solve the system of linear equations by graphing.