Question
the point (5,-3) is a solution to which system of equations
Answers
Answer
y = x + 2 and y = x + 5
Answer
y = x - 8 and 2x + y = 7
Answer
How man solutions does the system of equations have?
y = -2x + 12 and 4y + x - 20 = 0
y = -2x + 12 and 4y + x - 20 = 0
Answered by
GPT 3.5
Without the equations given, it is not possible to determine which system of equations contains the point (5,-3) as a solution. Please provide the equations so that I can assist you further.
Answered by
GPT 3.5
To determine if the point (5, -3) is a solution to the system of equations, we can substitute the x-coordinate and y-coordinate of the point into each equation and see if both equations are satisfied.
Substituting x = 5 into the first equation:
y = x + 2
-3 = 5 + 2
-3 = 7
The equation -3 = 7 is not true, so the point (5, -3) is not a solution to the equation y = x + 2.
Substituting x = 5 into the second equation:
y = x + 5
-3 = 5 + 5
-3 = 10
The equation -3 = 10 is not true, so the point (5, -3) is not a solution to the equation y = x + 5.
Therefore, the point (5, -3) is not a solution to the system of equations y = x + 2 and y = x + 5.
Substituting x = 5 into the first equation:
y = x + 2
-3 = 5 + 2
-3 = 7
The equation -3 = 7 is not true, so the point (5, -3) is not a solution to the equation y = x + 2.
Substituting x = 5 into the second equation:
y = x + 5
-3 = 5 + 5
-3 = 10
The equation -3 = 10 is not true, so the point (5, -3) is not a solution to the equation y = x + 5.
Therefore, the point (5, -3) is not a solution to the system of equations y = x + 2 and y = x + 5.
Answered by
GPT 3.5
To determine if the point (5, -3) is a solution to the system of equations, we can substitute the x-coordinate and y-coordinate of the point into each equation and see if both equations are satisfied.
Substituting x = 5 and y = -3 into the first equation:
y = x - 8
-3 = 5 - 8
-3 = -3
The equation -3 = -3 is true, so the point (5, -3) is a solution to the equation y = x - 8.
Substituting x = 5 and y = -3 into the second equation:
2x + y = 7
2(5) + (-3) = 7
10 - 3 = 7
7 = 7
The equation 7 = 7 is true, so the point (5, -3) is a solution to the equation 2x + y = 7.
Therefore, the point (5, -3) is a solution to the system of equations y = x - 8 and 2x + y = 7.
Substituting x = 5 and y = -3 into the first equation:
y = x - 8
-3 = 5 - 8
-3 = -3
The equation -3 = -3 is true, so the point (5, -3) is a solution to the equation y = x - 8.
Substituting x = 5 and y = -3 into the second equation:
2x + y = 7
2(5) + (-3) = 7
10 - 3 = 7
7 = 7
The equation 7 = 7 is true, so the point (5, -3) is a solution to the equation 2x + y = 7.
Therefore, the point (5, -3) is a solution to the system of equations y = x - 8 and 2x + y = 7.
Answered by
GPT 3.5
To determine the number of solutions the system of equations has, we can write the equations in slope-intercept form (y = mx + b) and compare their slopes.
The first equation y = -2x + 12 is already in slope-intercept form, with a slope of -2.
The second equation 4y + x - 20 = 0 can be rearranged to y = -(1/4)x + 5, which is also in slope-intercept form, but with a slope of -1/4.
Since the slopes of the two lines are different (-2 and -1/4), the lines will intersect at a single point.
Therefore, the system of equations has one solution.
The first equation y = -2x + 12 is already in slope-intercept form, with a slope of -2.
The second equation 4y + x - 20 = 0 can be rearranged to y = -(1/4)x + 5, which is also in slope-intercept form, but with a slope of -1/4.
Since the slopes of the two lines are different (-2 and -1/4), the lines will intersect at a single point.
Therefore, the system of equations has one solution.
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