SAT Nonlinear equations Question

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Question 1 · Medium · MathOctober 2024 Batch 2 · Q14Nonlinear equations in one variable and systems of equations in two variables · 0 solved

$y = 2 x^{2} - 15 x + 23$ $y = x + a$ In the given system of equations, $a$ is a constant. The graphs of the equations in the given system intersect at exactly one point, $(x, y)$ , in the $x y$ -plane. What is the value of $x$ ?

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The trap here

SAT discriminant: how many solutions, without solving — When an SAT question asks for exactly one solution or no real solution, it is asking about b² − 4ac. Solving the quadratic is the slow way to get it wrong.