Скачать или смотреть Digital SAT Math – Algebra (Hard) | Find Constant t for Parallel Lines | ID: f75bd744

n this problem, we’re asked to find the value of t so that the given system of equations has no solution.
No solution means the two lines are parallel — their slopes are the same, but the constants are different.
Let’s simplify both equations and use the coefficient-ratio rule to determine t quickly!

💡 Key Concept
For two linear equations:
a₁x + b₁y = c₁
a₂x + b₂y = c₂
*Parallel lines → a₁/a₂ = b₁/b₂ ≠ c₁/c₂
*Same line → a₁/a₂ = b₁/b₂ = c₁/c₂
*Intersecting lines → a₁/a₂ ≠ b₁/b₂
Here, simplifying both equations gives matching slope ratios and shows that t = 8.

✏️ Study Tip (Pop-Up Ideas)
1️⃣ If a system has “no solution,” it means the lines are parallel!
2️⃣ Parallel → same slope ratio (a₁/a₂ = b₁/b₂), different constant ratio (c₁/c₂).
3️⃣ Watch how the equations are simplified — the trick is to align coefficients first!

📘 Selected from the official College Board Digital SAT practice questions.
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