A system of equations gives two conditions that the same pair of numbers must satisfy. In Desmos, graph each equation as written and click where the lines cross to find that pair. Then check which coordinate the question asks for: in , comes first. Reading the second coordinate would answer a different question.
Hints
- Hint 1
A solution to a system must make both equations true at once. Each equation draws a line in Desmos. Where would you look for a point that lies on both lines?
- Hint 2
An ordered pair lists the -coordinate first and the -coordinate second. After you click where the lines cross, which number answers the question?
Step-by-step
Approach 1: Graph the two equations in Desmos
Step 1Graph the first equation
Type into Desmos. Its line shows pairs whose coordinates add to , but one line alone doesn't tell you which pair also satisfies the other equation.
- Step 2
Graph the second equation
Add on the next line as written. Desmos draws a second line. Where the lines cross, the same pair satisfies both equations.
- Step 3
Read the requested coordinate
Click the intersection, where the two lines cross. Desmos labels it . In , the first coordinate is , so read the coordinate asked for, not the whole pair. The value of is . Choice C.
Approach 2: Count equal parts by hand
Step 1Replace x with its equal expression
The second equation says , so replace in with : . This counts three -sized parts for and one more for .
- Step 2
Combine the parts
Combine the like terms, which are both multiples of : . The total has four parts, not three; leaving out the extra would change the equation.
- Step 3
Find the size of one part
Divide both sides by to find one part: .
- Step 4
Find x
Put into to find the requested value: . So the value of is . Choice C.