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Answer:
D. Infinitely many solutions
Explanation:
To compare two linear equations, it is handy to have them in the same for. It doesn't really matter what that form is. You generally want to reduce the equations as far as possible by removing any common factors from the coefficients.
Here, we can put both equations into standard form: ax +by = c.
First equation:
y = -3x +5 . . . . given
3x +y = 5 . . . . add 3x
Second equation:
6x +2y = 10 . . . . given
3x + y = 5 . . . . divide by 2
These two equations are now identical. That means they describe the same line, so any (x, y) pair that satisfies one of these equation will also satisfy the other one (obviously). That means there are an infinite number of points these lines have in common, an infinite number of solutions.
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More about number of solutions
Above is one of the possibilities.
Another possibility is that the left side looks the same, but the right side is different. For example, ...
3x +y = 5
3x +y = 4
The ratios of the coefficients of x and y are the same (a:b = 3:1). That means these lines have the same slope and they are the equations of parallel lines. They do not intersect, so this set of equations will have no solutions.
Another suitable form for comparing the slopes is slope-intercept form. The above two equations in that form would be ...
y = mx + b
y = -3x +5
y = -3x +4 . . . . . . same slope, different y-intercept
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If the equations are different (except as just noted), there is one solution. Lines with different slopes must cross somewhere. They will cross exactly once.