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Determine whether the system has one solution, no solution, or infinitely many...

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tipha | Student, Grade 9 | (Level 2) eNoter

Posted November 30, 2011 at 7:37 AM via web

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Determine whether the system has one solution, no solution, or infinitely many solutions:?

Determine whether the system has one solution, no solution, or infinitely many solutions: y = 2/3x

2x - y = -4

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dwbettine | Middle School Teacher | (Level 2) Adjunct Educator

Posted November 30, 2011 at 9:42 AM (Answer #1)

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In this system of equations, it will help if you arrange both equations into slope-intercept form, that is y = mx + b form. The first one is already in that form and indicates a slope of 2/3. The second equation arranged in slope-intercept form becomes y = 2x + 4 and has a slope off 2. Since these two linear functions have different slopes, they are not parallel so they MUST intersect. They intersect in exactly one point, which means they have one solution. That is to say, there is only one point, or ordered pair, which will satisfy both equations. The order pair is (-3,-2).

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