UPSKILL MATH PLUS

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Theory:

One of the methods of solving the simultaneous linear equations is the substitution method.

Let us learn how to solve the system of linear equations using the substitution method.
The steps to solve the system of linear equations using the substitution method is given by:

Step 1: From the given two equations, consider an equation. Find the value of one of the variables in terms of the other.

Step 2: Substitute the value (obtained in Step 1) in the other equation.

Step 3: Now, simplify the equation and find the value of the other unknown variable.

Step 4: Substituting the obtained value (variable in Step 3) in the equation (obtained in Step 1), we get the value of the first unknown variable.
To understand the concept clearly, let us consider an example.
Example:
Solve the simultaneous linear equations $$2x+y = 8$$ and $$x+2y = 10$$ by substitution method.

Solution:

Step 1: Consider an equation and find the value of one of the variables in terms of the other.

Consider the equation $$2x+y = 8$$

Subtract $$2x$$ from both the sides, we get:

$$2x+y-2x = 8-2x$$

$$y = 8-2x$$

Step 2: Substitute the value of $$y$$ in the other equation.

$$x+2(8-2x) = 10$$ (Substituting $$y = 8-2x$$)

Step 3: Solve the above equation and find the value of the variable $$x$$.

$$x+16-4x = 10$$

$$-3x+16 = 10$$

$$-3x = 10-16$$

$$-3x = -6$$

$$x = 2$$

Therefore, the value of one of the variables is $$x = 2$$.

Step 4: Substitute the value of $$x$$ in equation obtained in step 1.

Thus, substituting $$x = 2$$ in the equation $$y = 8-2x$$, we have:

$$y = 8-2(2)$$

$$y = 8-4 = 4$$

Therefore, the value of the other variable is $$y = 4$$.

Hence, the solution of the given system of equations is $$x = 2$$ and $$y = 4$$.