Question:
The graphs of the equations \( 2x + 3y = a \) and \( x + 2y = b \) intersect at a point \( P(\alpha, \beta) \). What is the value of \( (3\alpha + 2\beta) \)?
The graphs of the equations \( 2x + 3y = a \) and \( x + 2y = b \) intersect at a point \( P(\alpha, \beta) \). What is the value of \( (3\alpha + 2\beta) \)?
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When solving systems of linear equations, use substitution or elimination to find the point of intersection.
Updated On: Apr 17, 2025
- \( 5a - 8b \)
- \( 5a + 8b \)
- \( 4a + 5b \)
- \( 4a - 5b \)
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The Correct Option is D
Solution and Explanation
First, solve the system of equations to find the values of \( \alpha \) and \( \beta \). Then, substitute them into the expression \( (3\alpha + 2\beta) \) to calculate the value.
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