Question

How do you solve the system 2x + y = 1 and x + 2y = - 2 by graphing?

Answer 1

Hint: We will first find two points referring to line 1 and then find two points which lie on line 2. Then, we will join those points to form those lines and thus find the point of intersection in the graph.

Complete step by step solution:
We are given that we are required to solve the system 2x + y = 1 and x + 2y = - 2 by graphing.
Now, let us first consider the equation 2x + y = 1.
If, here, we put in x = 0, then we get y = 1 and if we put in x = 1, then we get y = - 1.
Thus, we have the following table for this equation:-

x	0	1
y	1	-1

Plotting this line, we will now obtain the following:-

Now, let us first consider the equation x + 2y = - 2.
If, here, we put in x = 0, then we get y = - 1 and if we put in x = - 2, then we get y = 0.
Thus, we have the following table for this equation:-

x	0	-2
y	-1	0

Plotting this line, we will now obtain the following:-

Now, if we plot these lines together, we will obtain the following graph.

Since, we can observe that these lines intersect at $\left( {\dfrac{4}{3}, - \dfrac{5}{3}} \right)$. Therefore, the solution is $x = \dfrac{4}{3}$ and $y = - \dfrac{5}{3}$ .

Note: The students must note that if not mentioned, that we need to solve it by graphing, we have an alternate method to do the same as well.
Since, we have 2x + y = 1 as the equation of first line.
Taking 2x from addition in the left hand side to subtraction in the right hand side, we will them obtain the following equation:-
$ \Rightarrow $y = 1 – 2x
Putting this value of y in the equation given by x + 2y = - 2, we will then obtain the following equation:-
$ \Rightarrow $x + 2 (1 – 2x) = - 2
Simplifying the calculations:-
$ \Rightarrow $x + 2 – 4x = - 2
Taking 2 from addition in the left hand side to subtraction in right hand side and clubbing the terms with x, we will then obtain the following equation:-
$ \Rightarrow $- 3x = - 4
Hence, $x = \dfrac{4}{3}$
Therefore, we have: $y = 1 - \dfrac{8}{3} = - \dfrac{5}{3}$.