Answer:
- 4x -2y +6 = 0
- y/3 -x/1.5 = 1
Explanation:
A system of two linear equations has an infinite number of solutions if the equations are dependent. That is, they describe the same line. Each equation can be rearranged to be identical to the other.
Example
4x -2y +6 = 0 . . . . . . general form equation
y/3 -x/1.5 = 1 . . . . . . intercept form equation
Both of these can be rearranged to the slope-intercept form equation ...
y = 2x +3
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Because these equations describe the same line, one of them is shown "dotted" in the attached graph.
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Additional comment
A "standard form" equation looks like ...
ax +by = c
where a ≥ 0, and a, b, c are mutually prime (integers). If a=0, then b > 0.
A "general form" equation looks like ...
ax +by +c = 0
Most descriptions of general form place no constraints on a, b, c, except to say that 'a' and 'b' cannot both be zero. It usually works well to "reduce" it so the coefficients are mutually prime (integers).
Of course, neither of these forms can have integer coefficients if the slope is an irrational number.