At an orbital tracking station, Emek and Tara monitored two satellites preparing to exchange a communication signal. On the station's coordinate map, Satellite A followed the projected path y = 2x + 1, while Satellite B followed y = -x + 10. The signal had to be transferred where the two paths intersected. Since both equations already gave y, Tara set their expressions equal: 2x + 1 = -x + 10. Solving gave x = 3, and substituting this value into the first equation gave y = 7. Emek checked the point in the second equation and also obtained 7, confirming that (3, 7) lay on both paths. The crew scheduled the signal transfer for that crossing point. When the satellites reached the predicted location, the transfer occurred as planned, and the tracking station recorded a successful connection.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
At the intersection, both equations have the same x-value and the same y-value.
Satellite A follows y = 2x + 1 and Satellite B follows y = -x + 10. Which equation should Tara solve to find the x-coordinate where the two paths intersect?
2x + 1 = x + 102x + 1 = -x + 102x - 1 = -x - 102x + 1 = -x - 10
Correct! Since both expressions equal y, setting them equal finds the x-coordinate of the intersection.
Not quite. Set the two expressions for y equal to each other without changing their signs.
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Hint
Substitute x = 3 into Satellite A's equation y = 2x + 1.
Tara solves 2x + 1 = -x + 10 and finds x = 3. What y-value does Satellite A have at x = 3?
Correct! Substituting x = 3 gives y = 7.
Try again. Replace x with 3 in y = 2x + 1 and simplify.
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🎉 Congrats! You got this question!
Hint
Substitute the x-coordinate 3 into each equation and check whether both produce the y-coordinate 7.
The station wants to verify that the signal transfer point (3, 7) lies on both satellite paths. Which calculation correctly checks the point in both equations?
Satellite A: 2(7) + 1 = 15; Satellite B: -7 + 10 = 3Satellite A: 2(3) + 1 = 6; Satellite B: -3 + 10 = 10Satellite A: 2(3) + 1 = 7; Satellite B: -3 + 10 = 7Satellite A: 2(7) + 3 = 17; Satellite B: -7 + 3 = -4
Correct! Both equations give y = 7 when x = 3, so (3, 7) lies on both paths.
Not quite. Use x = 3 in each equation and check whether each result equals 7.
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Uyduların Kesişme Noktası
TR
ARC_G09_PA_02_STORY_01
Uyduların Kesişme Noktası
The Satellite Crossing Point
EN
ARC_G09_PA_02_STORY_01
The Satellite Crossing Point