Mastering the Substitution Method | Simplifying and Solving Equations in Mathematics

Substitution

Substitution is a fundamental concept in mathematics that involves replacing a variable or expression in an equation or formula with a different variable or expression that has the same value

Substitution is a fundamental concept in mathematics that involves replacing a variable or expression in an equation or formula with a different variable or expression that has the same value. This technique is used to simplify or solve equations and expressions.

The process of substitution is particularly useful when dealing with equations that involve multiple variables. By substituting one variable with an equivalent expression, we can reduce the number of variables in the equation, making it easier to solve.

To illustrate the process of substitution, let’s consider the following example:

Suppose we have the equation:
3x + 2y = 10

And we also have the second equation:
y = 2x – 3

In order to solve this system of equations, we can use the substitution method. We start by solving the second equation for y, which gives us an expression that we can substitute into the first equation:

y = 2x – 3

Next, we substitute this expression for y in the first equation:

3x + 2(2x – 3) = 10

Now we can simplify the equation by distributing the 2:
3x + 4x – 6 = 10

Combining like terms:
7x – 6 = 10

Finally, we isolate x by adding 6 to both sides of the equation:
7x = 16

Dividing both sides by 7:
x = 16/7

Now that we have found the value of x, we can substitute it back into the second equation to solve for y:

y = 2(16/7) – 3
y = 32/7 – 3

Simplifying:
y = 32/7 – 21/7
y = 11/7

Therefore, the solution to the system of equations is x = 16/7 and y = 11/7.

In summary, substitution is a powerful technique in mathematics that allows us to replace variables or expressions in equations to simplify or solve them. This method is commonly used when dealing with systems of equations and helps us find the values of variables in a systematic way.

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