Question 379·Easy·Algebra

0 / 700

The system of equations is

$x + y = 10$

$x - y = 2$

What is the solution $(x, y)$ to the given system of equations?

A system of equations gives two rules for the same $x$ and $y$ . Type both equations into Desmos and click their intersection, the point where the lines cross. Read its coordinates in order: $x$ first, $y$ second. A pair that fits one equation can still be wrong, so make sure it fits both equations.

Hints

Hint 1
A system requires the same $x$ and $y$ to satisfy both equations. A pair that has the right sum might have the wrong difference. Where would a point satisfying both rules appear on the graphs?
Hint 2
The intersection is where the two lines cross. Type each equation into Desmos as written, then click that point. Read the first coordinate as $x$ and the second as $y$ .

Step-by-step

Approach 1: Click the intersection in Desmos
Step 1
Graph the sum equation
Type $x+y=10$ into Desmos. Its graph is a line: every point on it has coordinates whose sum is $10$ . You still need the second equation to pick out one point.
Step 2
Read the point on both lines
Add $x-y=2$ on a new line and click the intersection. Desmos shows $(6,4)$ . The intersection lies on both lines, so its coordinates make both equations true. In $(x,y)$ , $x$ comes first and $y$ comes second. The solution is $(6,4)$ . Choice B.

Approach 2: Cancel the opposite terms by hand
Step 1
Eliminate y
The $+y$ and $-y$ terms are opposites. Use elimination: add the equations so those terms cancel:
$(x+y)+(x-y)=10+2$
Combine the remaining terms:
$2x=12$
Step 2
Find x
Divide both sides by $2$ to get $x$ :
$x=\frac{12}{2}$
Evaluate:
$x=6$
Step 3
Find y and write the pair
Put $x=6$ into the first equation:
$6+y=10$
Subtract $6$ from both sides:
$y=4$
An ordered pair lists $x$ before $y$ , so the solution is $(6,4)$ . Choice B.

Question 379·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this