Question 163·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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The system of equations is

x = -3 \\[1.4em] y = 2x^2 + 5

A solution to the system of equations is $(x, y)$ . What is the value of $xy$ ?

In a system of equations, a solution $(x,y)$ satisfies both equations. If one equation gives $x$ outright, graph both in Desmos and click their intersection to find $y$ . Then calculate the expression the question asks for. The $y$ -coordinate alone isn't $xy$ , and a negative $x$ affects the product's sign.

Hints

Hint 1
A solution is a point that satisfies both equations. Graph $x=-3$ and $y=2x^2+5$ together. What point do the graphs share?
Hint 2
In $(x,y)$ , the first number is $x$ and the second is $y$ . The question asks for their product, not either coordinate alone. What sign will the product have?

Step-by-step

Graph the system, then multiply
Step 1
Find the point that satisfies both equations
Type $x=-3$ and $y=2x^2+5$ on separate lines in Desmos. Click their intersection, where the graphs meet. It shows $(-3,23)$ , so the point satisfying both equations has $x=-3$ and $y=23$ .
Step 2
Calculate the requested product
$xy$ means multiply $x$ and $y$ . Type $(-3)(23)$ on a new Desmos line; it shows $-69$ . The product is negative because $x$ is negative and $y$ is positive, so $xy=-69$ . Choice B.

Question 163·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this