Question 127·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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\begin{aligned} x + y &= 7 \\[1.4em] xy &= 10 \end{aligned}

If $x \ge y$ , what is the value of $x$ ?

Your answer

A nonlinear system has two equations with the same unknowns, where at least one equation isn't a line. Graph both equations in Desmos and click every intersection; each point satisfies both equations. A sum and a product can stay the same when the numbers switch places. Apply the ordering condition after finding the possible pairs, or you may choose the smaller value for $x$ .

Hints

Hint 1
A solution to a system is a pair of numbers that makes both equations true. On a graph, an intersection lies on both equations, so check every intersection before choosing a pair.
Hint 2
In a point $(x,y)$ , the first coordinate is $x$ . Compare it with the second coordinate using $x\ge y$ . Which point puts the larger number first?

Step-by-step

Approach 1: Graph both equations in Desmos
Step 1
Recognize why there may be two pairs
Switching $x$ and $y$ changes neither their sum nor their product. So if one pair works, its reversed order works too. The condition $x\ge y$ will tell you which order to use.
Step 2
Read the intersections and choose
Type both equations into Desmos and click both intersections. Desmos shows $(2,5)$ and $(5,2)$ . The first coordinate is $x$ ; only $(5,2)$ has $x\ge y$ . So the requested value of $x$ is $5$ . Grid in 5.

Approach 2: Find the sum-and-product pair
Step 1
Find the two numbers
A factor pair gives two numbers whose product is $10$ . The pair $2$ and $5$ also has the required sum of $7$ :
$2\times5=10,\qquad 2+5=7.$
Step 2
Put the numbers in the required order
Because $x\ge y$ , the larger number goes in the $x$ position. Assign $x=5$ and $y=2$ , so the value of $x$ is $5$ . Grid in 5.

Question 127·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