Solve the system of equations by graphing. Then classify the system.
f(x)=x+1
g(x)=-8x+10
What is the solution of the system?
a)The solution is___?
b)There are infinitely many solutions
c)There is no solution
Is the system consistent or inconsistent?
a)inconsistent
b)consistent
Are the equations dependent or independent?
a)dependent
b)independent
solve the following system of equation by graphing.
1.4x+y=7, 3x+y=7
2. y=2x, y=-x-6
Thank You
To solve the system of equations by graphing, we will graph the two equations f(x) = x+1 and g(x) = -8x+10. Then we will find the point where the two lines intersect, which will represent the solution to the system.
First, let's graph the equation f(x) = x+1. This is a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 1 and the y-intercept is 1. So, we can start by plotting the point (0,1) on the graph and then using the slope of 1 to find other points on the line.
Next, let's graph the equation g(x) = -8x+10. Again, this is a linear equation in the form y = mx + b. The slope is -8 and the y-intercept is 10. So, we can start by plotting the point (0, 10) on the graph and then using the slope of -8 to find other points on the line.
Now, we can graph the two equations on the same coordinate plane. The point where the two lines intersect is the solution to the system.
To classify the system, we need to analyze the graph. If the lines intersect at a single point, then the system has a unique solution. If the lines are coincident (they overlap and are the same line), then there are infinitely many solutions. If the lines are parallel and do not intersect, then there is no solution.
Now, let's analyze the graph and find the solution:
By graphing the two lines, we find that they intersect at the point (1, -7). This is the solution to the system of equations.
Now, let's classify the system:
The system has a unique solution, so the answer to the first question is:
a) The solution is (1, -7).
The system is consistent because there is a solution, so the answer to the second question is:
b) consistent.
The equations are independent because they each have a unique equation and are not multiples of each other. So the answer to the third question is:
b) independent.
In summary, the solution to the system is (1, -7). The system is consistent with independent equations.