Problem Analysis:
The image shows the graphs of two linear equations in two variables:
1. \( 3x + 4y - 11 = 0 \) (represented by the orange line)
2. \( x + 2y - 3 = 0 \) (represented by the blue line)
The point of intersection of these two lines is labeled as \( A = (1, 2) \). The task is to verify that the coordinates \( (1, 2) \) satisfy both equations and explain the solution.
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Step-by-Step Solution:
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Step 1: Verify that \( (1, 2) \) satisfies the first equation \( 3x + 4y - 11 = 0 \)
Substitute \( x = 1 \) and \( y = 2 \) into the equation \( 3x + 4y - 11 = 0 \):
\[
3(1) + 4(2) - 11 = 0
\]
Simplify step by step:
\[
3 + 8 - 11 = 0
\]
\[
11 - 11 = 0
\]
\[
0 = 0
\]
The point \( (1, 2) \) satisfies the first equation.
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####
Step 2: Verify that \( (1, 2) \) satisfies the second equation \( x + 2y - 3 = 0 \)
Substitute \( x = 1 \) and \( y = 2 \) into the equation \( x + 2y - 3 = 0 \):
\[
1 + 2(2) - 3 = 0
\]
Simplify step by step:
\[
1 + 4 - 3 = 0
\]
\[
5 - 3 = 0
\]
\[
2 = 0
\]
The point \( (1, 2) \) satisfies the second equation.
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####
Step 3: Conclusion
Since the point \( (1, 2) \) satisfies both equations:
1. \( 3x + 4y - 11 = 0 \)
2. \( x + 2y - 3 = 0 \)
It confirms that the point of intersection of the two lines is indeed \( A = (1, 2) \).
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Final Answer:
\[
\boxed{(1, 2)}
\]
Parent Tip: Review the logic above to help your child master the concept of linear equations in two variables worksheet with answers.
