Question 394·Easy·Algebra

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What ordered pair $(x,y)$ satisfies the system of equations?

\begin{aligned} x + y &= 5\\[1.4em] x - y &= 1 \end{aligned}

A system of equations gives two equations about the same unknowns, so its solution must make both true. Graph each equation as written in Desmos and click their intersection, the point shared by both lines. Read the intersection in $(x,y)$ order. A point on only one line, or a pair with its coordinates swapped, won't answer the question.

Hints

Hint 1
A solution to a system must satisfy both equations at once. On a graph, that means it lies on both lines. Where do the lines meet after you type the equations?
Hint 2
An ordered pair lists $x$ first and $y$ second. Click the intersection rather than estimating from the grid. Which number is the $x$ -coordinate?

Step-by-step

Approach 1: Click the Desmos intersection
Step 1
Graph both equations
Type $x+y=5$ and $x-y=1$ on separate lines in Desmos. The graphs cross once. Their intersection is the point shared by both lines, so it makes both equations true.
Step 2
Read the pair in order
Click the intersection. Desmos shows $(3,2)$ : the first coordinate is $x=3$ , and the second is $y=2$ . The ordered pair satisfying the system is $(3,2)$ . Choice B.

Approach 2: Add to cancel a variable
Step 1
Cancel the opposite terms
The equations have $+y$ and $-y$ . Add the whole equations, keeping the left sides together and the right sides together, so those opposite terms cancel:
$(x+y)+(x-y)=5+1$ $2x=6$
Step 2
Find the first coordinate
Divide both sides by $2$ to find the x-coordinate, the first number of the pair:
$x=3$
Step 3
Use the first equation
Put $x=3$ into the first equation to find $y$ :
$3+y=5$
Step 4
Finish the ordered pair
Subtract $3$ from both sides to find the y-coordinate:
$y=2$
So the pair satisfying the system is $(3,2)$ . Choice B.

Question 394·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this