Question 1
How many solutions does the following system of equations have?
\[\begin{aligned} y &= x^2 \\ y &= 4 \end{aligned}\]
Easy - Quiz 1
Work through systems that pair a linear equation with a quadratic or other nonlinear equation using substitution and basic reasoning.
Question 1 of 5
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Answer question 1 to unlock
What is the sum of the \(y\)-coordinates of all solutions to the following system?
\[\begin{aligned} y &= x^2 - 1 \\ y &= 3 \end{aligned}\]
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A gym offers two membership plans. Plan A charges a flat fee of \(y = 50\) dollars per month. Plan B charges based on the number of visits \(x\) per month according to \(y = 0.5x^2\). For what number of visits do the two plans cost the same?
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Answer question 3 to unlock
What are the solutions to the following system of equations?
\[\begin{aligned} y &= x + 2 \\ y &= x^2 \end{aligned}\]
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Answer question 4 to unlock
A company models its daily revenue \(R\) and daily cost \(C\), both in dollars, using the equations below, where \(x\) is the number of units sold.
\[\begin{aligned} R &= 12x \\ C &= x^2 + 20 \end{aligned}\]
At what values of \(x\) does the company break even?