Part 1: Provide a system of TWO equations in slope-intercept form, with only one solution. Using complete sentences, explain why this system has one solution. Part 2: Provide a system of TWO equations in slope-intercept form with no solutions. Using complete sentences, explain why this system has no solutions. Part 3: Provide a system of TWO equations in slope-intercept form with infinitely many solutions. Using complete sentences, explain why this system has infinitely many solutions.
Wow, I had to do something just like this, except it was for linear algebra
I won't xD
1) y = x y = -x + 2 The lines representing both equations intersect only once on the xy-axis, so there is only one solution. 2) y = x y = x + 2 The lines representing both equations are parallel lines since they have the same gradient. However, they do not intersect each other, so there is no solution. 3) y = x 2y = 2x Both equations represent the same line, so every point on the line is a solution. Since the line is infinitely long, the number of solutions is also infinitely many.
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