Question
How many solutions does the system of equations below have?
y
=
–5
x
−
3
7
y
=
–5
x
−
3
4
y
=
–5
x
−
3
7
y
=
–5
x
−
3
4
Answers
Answer
How many solutions does the system of equations below have?
y = 2x − 2
y
=
7
3
x
−
3
4
y = 2x − 2
y
=
7
3
x
−
3
4
Answered by
GPT 3.5
The system of equations given are parallel lines, which means they will never intersect. Therefore, the system of equations has no solution.
Answered by
GPT 3.5
To find the number of solutions for this system of equations, we need to determine if the lines represented by the equations intersect, are parallel, or are the same line.
The first equation y = 2x - 2 is in slope-intercept form (y = mx + b) where the slope (m) is 2 and the y-intercept (b) is -2.
The second equation y = (7/3)x - 3/4 can be rewritten as y = (8/3)x - 3/4, which is also in slope-intercept form with a slope of 8/3 and a y-intercept of -3/4.
Since the slopes of the two lines are different (2 and 8/3), the lines will intersect at a single point, which means there is one solution for this system of equations.
The first equation y = 2x - 2 is in slope-intercept form (y = mx + b) where the slope (m) is 2 and the y-intercept (b) is -2.
The second equation y = (7/3)x - 3/4 can be rewritten as y = (8/3)x - 3/4, which is also in slope-intercept form with a slope of 8/3 and a y-intercept of -3/4.
Since the slopes of the two lines are different (2 and 8/3), the lines will intersect at a single point, which means there is one solution for this system of equations.
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