Question

For 15 points.Explain, in your own words, the steps necessary to solve a system of equations

using the substitution method.

Answer 1

★ Required Answer:-

First, what is an equation?

➳ A mathematical statement which shows that two algebraic expressions are equal is called and equation.

Or, LHS = RHS

Example:- 3x - 5 = x + 8

An equation is said to be a linear equation if it contains only one variable (literal) with highest power 1.

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Solving an equation:-

To solve the equation x + 5 = 7 means to find the value of an unknown algebraic quantity used in the equation.

Example:-

• To solve the equation x + 5 = 7 means to find the value of x.
• To solve the equation 3y + 2 = 9 means to find the value of y.
• To solve the equation
  `\sf (2a)/(3) + 4 = 10` means to find the value of a ⠀⠀⠀⠀⠀⠀and so on!

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★ Rules for solving an equation by the substitution method:-

Rule ❶

If x = 2, the value of the expression 3x + 2 = 3 × 2 + 2 = 6 + 2 = 8

Rule ❷

If x = 0, the value of the expression 3x + 2 = 3 × 0 + 2 = 0 + 2 = 2

Rule ❸

If x = -2, the value of the expression 3x + 2 = 3 × -2 + 2 = -6 + 2 = -4

Now consider the algebraic expression 5x - 2y

This expression consists of variables x and y.

Now if :-

• x = 3 and y = 2, 5x - 2y = 5 × 3 2 × 2 = 15 - 4 = 11
• x = 8 and y = 5, 5x - 2y = 5 × 8 - 2 × 5 = 40 - 10 = 30

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The process of finding the value of an algebraic expression by substituting the given value of its variable is called substitution.⠀⠀