Write an equation of the line in slope-intercept form
1 answer:
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Answer:
a. No solution, parallel lines.
b. One solution.
Step-by-step explanation:
Given the system of equations:
a.
b.
To give a geometric description of the given system of equations.
The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.
i.e.
Number of planes = Number of variables
Number of lines = Number of equations in the system.
Here, we are given 2 variables and 2 equation in each system.
So, they can be represented in the xy-coordinates plane.
And the number of solutions to the system depends on the following condition.
Let the system of equations be:
1. One solution:
There will be one solution to the system of equations, If we have:
2. Infinitely Many Solutions: (Identical lines in the system)
3. No Solution:(Parallel lines)
Now, let us discuss the system of equations one by one:
a. OR
OR
Here, the ratio:
Therefore, no solution i.e. parallel lines.
b. OR
OR
So, one solution.
Kindly refer to the images attached for the graphical representation of the given system of equations.
