Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Answer:
Step-by-step explanation:
To solve the simultaneous equations using the elimination method, we start with the given equations:
1. \( 5x - y = 18 \)
2. \( x + y = 6 \)
First, we'll eliminate one of the variables by adding or subtracting the equations. Let's eliminate \( y \) by adding the two equations together.
Adding equation (1) and equation (2):
\[ (5x - y) + (x + y) = 18 + 6 \]
Simplify the left side:
\[ 6x = 24 \]
Now, solve for \( x \):
\[ x = \frac{24}{6} \]
\[ x = 4 \]
Now that we have \( x = 4 \), substitute this value back into equation (2) to find \( y \):
\[ 4 + y = 6 \]
Subtract 4 from both sides:
\[ y = 6 - 4 \]
\[ y = 2 \]
So, the solutions to the simultaneous equations are \( x = 4 \) and \( y = 2 \).
To verify:
Substitute \( x = 4 \) and \( y = 2 \) back into equation (1):
\[ 5(4) - 2 = 20 - 2 = 18 \]
Equation (1) holds true.
Substitute \( x = 4 \) and \( y = 2 \) back into equation (2):
\[ 4 + 2 = 6 \]
Equation (2) also holds true.
Therefore, the solution to the simultaneous equations using the elimination method is \( \boxed{(4, 2)} \).
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
