Problem 11 Determine whether each equation ... [FREE SOLUTION]

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Chapter 15: Problem 11

Determine whether each equation has the given ordered pair as a solution. \(a-5 b=-3 ;(2,1)\)

Short Answer

Expert verified

(2,1) is a solution because substituting the values into the equation makes both sides equal.

Step by step solution

Understand the Given Equation

Analyze the given equation, which is in the form of a linear equation: a - 5b = -3.

Identify the Ordered Pair

The ordered pair given is (2,1), which means a = 2 and b = 1.

Substitute the Values into the Equation

Substitute a = 2 and b = 1 into the equation:a - 5b = -32 - 5(1) = -3

Simplify the Equation

Simplify the equation after substitution:2 - 5(1) = 2 - 5 = -3

Verify the Result

Compare the simplified result with the original equation's right-hand side:-3 = -3Since both sides are equal, (2,1) is a solution of the equation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

ordered pairs

In the context of linear equations, an **ordered pair** is a set of values that can be substituted into the equation to verify if they satisfy it.
Ordered pairs are written in the form (a, b), where 'a' and 'b' are specific values.
For example, the ordered pair (2, 1) means 'a' is 2 and 'b' is 1. In other words, these values are tested in place of the variables.
This helps to see if the equation holds true with these specific numbers.

substitution method

The **substitution method** involves replacing the variables in an equation with the values from an ordered pair.
In our exercise, the equation is a - 5b = -3.
We substitute 'a' with 2 and 'b' with 1, turning the equation into:
2 - 5(1) = -3
This step helps us understand if these values make the equation true. The substitution is straightforward, making the abstract equation more concrete and easier to manage.

simplification

After substitution, we need to **simplify** the equation. Simplification means performing arithmetic operations to make the equation easier to understand.
In our example:
2 - 5(1) becomes 2 - 5.
Next, we simplify further by calculating the result:
2 - 5 = -3
Simplifying helps to reduce the equation to a single understandable expression, confirming if the values fit the equation.

solution verification

The final step is **solution verification**. This ensures that the simplified result matches the equation's original right-hand side.
In this instance, we compare the simplified result -3 with the right-hand side of the equation -3.
Both sides are equal, confirming (2,1) is indeed a valid solution.
Verification is critical to ensure our solution is correct.
It validates that we have followed all steps accurately and confirms the ordered pair satisfies the initial equation.

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91影视

Determine whether each equation has the given ordered pair as a solution. \(a-5 b=-3 ;(2,1)\)

Short Answer

Step by step solution

Understand the Given Equation

Identify the Ordered Pair

Substitute the Values into the Equation

Simplify the Equation

Verify the Result

Key Concepts

ordered pairs

substitution method

simplification

solution verification

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