Solve the system of equations by graphing then classify the system as consistent and the equation as dependent or independent.
4x-y=26
4x+5y=-10
What is the solution of the system of Equations?
(type am ordered pair Type N if there is no solution Type R if the solution is all real numbers)
It says it is wrong it is looking for 2 point per equation
To solve the system of equations by graphing, we need to graph both equations on the same coordinate plane and identify the point(s) of intersection. These points will represent the solutions to the system of equations.
Let's start with the first equation: 4x - y = 26.
To graph this equation, we will first rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Rearranging the equation, we get:
y = 4x - 26.
Now, we can plot the y-intercept at -26 and use the slope of 4 to plot additional points. In this case, since the coefficient of x is positive, the slope tells us to move up 4 units on the y-axis for every 1 unit we move to the right on the x-axis. Connect these points, and you have the graph of the first equation.
Now, let's move on to the second equation: 4x + 5y = -10.
Again, we will rearrange it in slope-intercept form:
5y = -4x - 10,
y = (-4/5)x - 2.
Plot the y-intercept at -2 and use the slope of -4/5 (negative slope) to plot additional points. Connect these points, and you have the graph of the second equation.
Now, we need to find the point of intersection between these two lines. This point represents the solution to the system of equations.
By graphing these two equations, you should find that the lines intersect at the point (-4, 3). Therefore, the solution to the system of equations is (-4, 3), which means x = -4 and y = 3.
To classify the system as consistent and the equations as dependent or independent, we can observe that the lines intersect at a unique point. This implies that the system is consistent (has a solution) and the equations are independent.
The solution to the system of equations is (-4, 3).