Respuesta :
Both equations y = 0.5x + 2.75 and y – 0.5x = 2.75 are equal. Hence, these systems will have infinite solutions. Hence, Option a is the most suitable answer to this question.
The system of equations having an infinite number of solutions must be the same.
In option a -
we have, y = 0.5x + 2.75 and 2y = x + 2.75
Rewriting the second equation 2y = x + 2.75 in slope-intercept form, we get,
2y = x + 2.75
y = x/2 + 2.75/2
y = 0.5x + 1.375
Both equations are not similar.
Hence this option is not the right choice.
Similarly, we will check for option b -
we have, y = 0.5x + 2.75 and y – 0.5x = 2.75
From the second equation y - 0.5x = 2.75, this can be expressed as y = 0.5x + 2.75 in the slope-intercept form.
Here, we get both equations equal.
Thus, y = 0.5x + 2.75 and y – 0.5x = 2.75 will have infinite solutions.
Similarly, checking for other options, we do not get any similar equations.
Hence, option b is the correct answer to this question.
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The complete question is -
Which systems have infinite solutions? Check all that apply.
a) y = 0.5x + 2.75 and 2y = x + 2.75
b) y = 0.5x + 2.75 and y – 0.5x = 2.75
c) y = 0.5x + 2.75 and 0.5x + y = 2.75
d) y = 0.5x + 2.75 and y = 0.5(x + 5.5)
e) y = 0.5x + 2.75 and y = –2(–0.25x )+ 2.75
