Solving Systems Graphically Find or create an example of a system of equations with one solution. Graph and label the lines on a coordinate plane. Provide their equations. State the accurate solution to the system.

postillan4 2021-08-04 Answered
Solving Systems Graphically- One Solution
Find or create an example of a system of equations with one solution.
Graph and label the lines on a coordinate plane. Provide their equations.
State the accurate solution to the system.

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Expert Answer

lobeflepnoumni
Answered 2021-08-05 Author has 26829 answers
Step 1
Consider a system of equation
\(\displaystyle{x}−{y}={2}\)
\(\displaystyle{x}+{y}={4}\)
Step 2
image
The solution of the system is
\(\displaystyle{x}={3}\)
\(\displaystyle{y}={1}\)
Step 3
We can also find the solution of system algebraically
\(\displaystyle{x}−{y}={2}\ldots\ldots.{\left({1}\right)}\)
\(\displaystyle{x}+{y}={4}\ldots\ldots.{\left({2}\right)}\)
From equation (1)
\(\displaystyle{x}−{y}={2}\)
\(\displaystyle{y}={x}−{2}\)
Put the value of y in equation (2)
\(\displaystyle{x}+{y}={4}\)
\(\displaystyle{x}+{x}−{2}={4}\)
\(\displaystyle{2}{x}−{2}={4}\)
\(\displaystyle{2}{x}={4}+{2}\)
\(\displaystyle{2}{x}={6}\)
\(\displaystyle{x}={3}\)
Put the value of x in equation (1)
\(\displaystyle{x}−{y}={2}\)
\(\displaystyle{3}−{y}={2}\)
\(\displaystyle{y}={3}−{2}\)
\(\displaystyle{y}={1}\)
Hence the solution is
\(\displaystyle{x}={3}\)
\(\displaystyle{y}={1}\)
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