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Part 1

Use substitution to determine whether the given ordered pairs are solutions of the given equation.

left parenthesis four thirds comma five fourths right parenthesis43,54​, 

left parenthesis 1 comma three halves right parenthesis1,32​; 

66xminus−44yequals=33

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Part 1

Is 

left parenthesis four thirds comma five fourths right parenthesis43,54 

a​ solution?

To determine whether the given ordered pair \(\left(\frac{4}{3}, \frac{5}{4}\right)\) is a solution of the equation \(6x - 4y = 3\), we will substitute \(x = \frac{4}{3}\) and \(y = \frac{5}{4}\) into the equation and check if it satisfies the equation.

Given equation:
\[
6x - 4y = 3
\]

Substitute \(x = \frac{4}{3}\) and \(y = \frac{5}{4}\) into the equation:

\[
6\left(\frac{4}{3}\right) - 4\left(\frac{5}{4}\right) = 3
\]

Now, calculate each term:

1. \(6 \times \frac{4}{3} = 2 \times 4 = 8\)
2. \(4 \times \frac{5}{4} = 5\)

So, the equation becomes:

\[
8 - 5 = 3
\]

Since \(3 = 3\), the equation holds true.

Therefore, the ordered pair \(\left(\frac{4}{3}, \frac{5}{4}\right)\) **is** a solution to the equation \(6x - 4y = 3\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How can substitution help in solving systems of equations?
2. What happens if an ordered pair does not satisfy the equation?
3. How would you solve the equation \(6x - 4y = 3\) for \(x\)?
4. Can an ordered pair satisfy multiple linear equations simultaneously?
5. What is the importance of checking multiple points in a linear equation?

**Tip:** When substituting fractions, simplifying the equation step by step helps in avoiding errors.

Learn how to verify if the ordered pair (4/3, 5/4) satisfies the linear equation 6x - 4y = 3 using the substitution method. This problem involves applying algebraic techniques to check the validity of solutions in high school level mathematics.

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