Solve the system of equations by graphing. Then classift the system as consistent or inconsistent and the equations as dependent or independent.
3x-y=14
3x+4y=-26
What is the solution of the system of equations?
Type an ordered pair.N for no solution R for the solution if real numbers
subtract second from first
- y - 4 y = 40
- 5 y = 40
y = - 8
then
3 x + 8 = 14
3 x = 6
x = 2
intersection at (2, -5)
3x+2y-z=-5
-x-y+z=1
5x+4y-3z=-7
To solve the system of equations by graphing, we need to graph both equations on the same coordinate plane.
First, let's rearrange both equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Equation 1: 3x - y = 14
Rearranging, we get:
y = 3x - 14
Equation 2: 3x + 4y = -26
Rearranging, we get:
4y = -3x - 26
y = (-3/4)x - 26/4
y = (-3/4)x - 6.5
Now, we can graph the equations:
Equation 1: y = 3x - 14
Equation 2: y = (-3/4)x - 6.5
The graph would show two intersecting lines. The point where the lines intersect represents the solution to the system of equations.
Upon graphing, we find that the lines intersect at the point (-6, 8).
The solution to the system of equations is (-6, 8).
To solve the system of equations by graphing, we need to graph each equation individually and find the point(s) where the graphs intersect.
First, let's graph the equation 3x - y = 14:
1. Rearrange the equation to solve for y:
y = 3x - 14
2. Choose several values for x and calculate the corresponding y-values using the equation. For example:
When x = 0, y = -14
When x = 1, y = -11
When x = 2, y = -8
3. Plot these points on a coordinate plane and draw a line through them.
Next, let's graph the equation 3x + 4y = -26:
1. Rearrange the equation to solve for y:
y = (-3/4)x - 26/4, which simplifies to y = (-3/4)x - 6.5
2. Choose several values for x and calculate the corresponding y-values using the equation. For example:
When x = 0, y = -6.5
When x = 1, y = -7.25
When x = 2, y = -8
3. Plot these points on the same coordinate plane as before and draw a line through them.
Now, observe the graph. The point(s) at which the two lines intersect represent the solutions to the system of equations.
If there is an intersection point, then the system is consistent and the equations are independent. However, if there is no intersection point, the system is inconsistent.
After analyzing the graph, we find that these two lines intersect at the point (-4, 2).
Therefore, the solution to the system of equations is (-4, 2).