Solve the system by graphing.
4x+2y=10
y=4
you must graph the line y = -2x + 5 and the horizontal line y = 4. The point at which their intersect is the solution to the system.
To solve the given system of equations by graphing, we need to graph both equations on the same coordinate plane and find the point where they intersect.
Let's start by graphing the equation 4x + 2y = 10.
To make it easier to graph, let's rewrite it in slope-intercept form.
4x + 2y = 10
2y = -4x + 10
y = -2x + 5
Now, we can plot the first equation on a graph:
Plotting the points:
x = 0, y = 5 (0, 5)
x = 1, y = 3 (1, 3)
x = 2, y = 1 (2, 1)
Draw a straight line passing through these three points.
Next, let's graph the equation y = 4.
Since y = 4 is a horizontal line passing through the y-axis at 4, we can just draw the line.
Now, let's observe the graph to see where the two lines intersect.
From the graph, we can see that the two lines intersect at the point (2, 4).
Therefore, the solution to the given system of equations is x = 2 and y = 4.
To solve the system of equations by graphing, we will graph both equations on the same coordinate plane and find the point of intersection (if it exists). This point represents the solution to the system.
The first equation is 4x + 2y = 10. To graph it, we need to first rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Start by isolating y:
4x + 2y = 10
2y = -4x + 10
y = -2x + 5
Now we have the equation in slope-intercept form. We can plot the graph of this line.
Next, let's look at the second equation, y = 4. This equation is already in slope-intercept form, with a slope of 0 and y-intercept of 4. The graph of this equation is a horizontal line passing through the y-coordinate of 4.
Now, graph both lines on the same coordinate plane. The first line, y = -2x + 5, will have a negative slope and pass through the y-intercept of 5. The second line, y = 4, will be a horizontal line passing through the y-coordinate of 4.
Once both lines are plotted, locate the point of intersection (if it exists). This point represents the solution to the system of equations.
In this case, by looking at the graphs, you will notice that the lines are parallel and do not intersect. This means that the system of equations does not have a solution. It is considered inconsistent.
Graphing is a visual method to determine the solution to a system of equations, but keep in mind that it is not always the most precise or accurate method. In some cases, the intersection point may be difficult to determine precisely. In such instances, it is helpful to use algebraic methods like substitution or elimination.