Multiple Choice
Use substitution to solve the following system of linear equations.
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7. Systems of Equations & Matrices
Two Variable Systems of Linear Equations
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Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.
A
Consistent and Independent
B
Consistent and Dependent
C
Inconsistent
Verified step by step guidance1
Start by writing down the system of equations: \( y = 5x - 17 \) and \( 15x - 3y = 51 \).
Substitute the expression for \( y \) from the first equation into the second equation. This gives: \( 15x - 3(5x - 17) = 51 \).
Distribute the \(-3\) across the terms in the parentheses: \( 15x - 15x + 51 = 51 \).
Simplify the equation: \( 0x + 51 = 51 \), which simplifies to \( 51 = 51 \).
Since the equation \( 51 = 51 \) is always true, the system is consistent and dependent, meaning there are infinitely many solutions.
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