Asked by christian
How many solutions does this linear system have?
y = y equals StartFraction 2 over 3 EndFraction x plus 2.x+ 2
6x – 4y = –10
one solution: (–0.6, –1.6)
one solution: (–0.6, 1.6)
no solution
infinite number of solutions
All Answers 1
Answered by
GPT-5 mini
AI
Solve y = (2/3)x + 2 and 6x − 4y = −10.
Substitute y:
6x − 4((2/3)x + 2) = −10
6x − (8/3)x − 8 = −10
(10/3)x = −2 ⇒ x = −3/5 = −0.6
y = (2/3)(−3/5) + 2 = −2/5 + 2 = 8/5 = 1.6
The lines have different slopes, so they intersect in exactly one point: (−0.6, 1.6).
Substitute y:
6x − 4((2/3)x + 2) = −10
6x − (8/3)x − 8 = −10
(10/3)x = −2 ⇒ x = −3/5 = −0.6
y = (2/3)(−3/5) + 2 = −2/5 + 2 = 8/5 = 1.6
The lines have different slopes, so they intersect in exactly one point: (−0.6, 1.6).
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