Two equations sharing and form a system: its solution makes both equations true. In Desmos, graph each equation as written and click their intersection, then read the coordinate the question asks for. If one equation already fixes a variable, substitution is a quick hand route; watch which variable is larger when the other has an added amount.
Hints
- Hint 1
A system needs a point that makes both equations true. The first equation fixes , so graphing it gives a line of points with the same first coordinate. What other line must the solution lie on?
- Hint 2
An intersection is where two graphs meet, so it gives a point that satisfies both equations. Click the intersection and read its second coordinate, not its first, to find .
Step-by-step
Approach 1: Read the intersection in Desmos
Step 1Graph the fixed x-value
The first equation fixes at . Type in Desmos. It draws a vertical line through , so every point on this line has the required first coordinate.
- Step 2
Read the coordinate the question asks for
Type on the next line, then click its intersection with . Desmos labels the point : it satisfies both equations. In , is the second coordinate. So the value of is . Choice D.
Approach 2: Use the value already given
Step 1Put 7 in place of x
Use substitution: since the first equation says , replace in the second equation with that same value:
- Step 2
Isolate y
Subtract from both sides to undo the beside :
So . The equation says is greater than , not the other way around. Choice D.