How to Solve Simultaneous Equations | Methods and Steps for Finding Solutions

Simultaneous Equations

Simultaneous equations refer to a system of equations that are solved together or simultaneously

Simultaneous equations refer to a system of equations that are solved together or simultaneously. These equations involve multiple variables and are used to find values that satisfy all the equations in the system.

The general form of a simultaneous equation with two variables (x and y) is:

a₁x + b₁y = c₁
a₂x + b₂y = c₂

where a₁, b₁, c₁, a₂, b₂, and c₂ represent constants.

To solve simultaneous equations, there are various methods including the substitution method, elimination method, and matrix method. Here, I will explain the substitution method:

1. Solve one of the equations for one variable. For example, if the first equation is solved for x, it would be x = (c₁ – b₁y) / a₁.

2. Substitute the value of the variable found in step 1 into the other equation. For example, if x = (c₁ – b₁y) / a₁, substitute this expression for x in the second equation. This will give you an equation with only one variable.

3. Solve the resulting equation from step 2 to find the value of the remaining variable.

4. Substitute the value found in step 3 back into either of the original equations to find the value of the other variable.

5. Check your solution by substituting the values obtained in step 3 and step 4 into both original equations. The solution should satisfy both equations.

It is important to note that simultaneous equations may have one unique solution, infinitely many solutions, or no solution depending on the given equations and variables involved.

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