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Solving Systems of Equations by Graphing

System of equations generally refers to the system of linear equations. A system of equation is a collection of linear equations sharing same set of variables. A system of linear equations can be solved by using various methods like:

  • Substitution Method
  • Elimination Method
  • Graphical Method
  • Matrix Method

Here, we are going to study about graphical method.

For solving a system of equation by graphical method, we need to follow the following steps:
Step 1: For the first equation, determine the value of one variable in terms of other.
Step 2: Now, choose random numbers and substitute them to find the value of given variables.
Step 3: Repeat the same process for other equation too.
Step 4: Draw a table out of given data.
Step 5: Mark all the points on graph for both the equations.
Step 6: Read the intersection point of the equations from the graph. This is the required solution.

We shall understand graphical method more precisely with the help of an example.

Example: Solve the following system of equations graphically:
2x + 3y = 5 and x + y = 2
2x + 3y = 5 ...........(1)
x + y = 2 ...............(2)
Find the value of y in terms of x

From equation (1), we get
$y$ = $\frac{5-2x}{3}$

From equation (2), we get
y = 2 - x

$y$ = $\frac{5-2x}{3}$ y = 2 - x

So, for equation (1), we get the points (-2, 3), (-1, 2.3), (0, 1.7) and (1, 1).
For equation (2), we get the points (-2, 4), (-1, 3), (0, 2) and (1, 1).
We obtain the following graph out of above points:

Solving Systems of Equations by Graphing

We can easily see that the two lines are intersecting at point (1, 1). Hence, the solution is:
x = 1 and y = 1.

Related Calculators
Solve a System of Equations Calculator

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