Which systems of equations have no solutions? (Check all that apply. ) x – y = 1, –3x 3y = 3 2y = 3 – 4x, x y = 0 12x 2 = 4y – 1
2 answers:
To solve such problems we need to know about the system of equatons.
<h3 /><h3>System of Equation</h3>When the lines of the system of the equation are parallel to each other the system of equations has no solution.
Two lines are parallel lines if they have the same slope and different y-intercept.
<h3>Given options</h3>A.) x – y = 1, –3x+3y = 3
B.) 2y = 3 – 4x, x+y = 0
C.) 12x+2 = 4y – 10, 2x+y = –11
D.) –3x – y = 5, 15x = 10 – 5y
E.) x+y = 1, –4x+2y = 7.
<h3 /><h3>Solutions</h3>A.) x-y=1, -3x+3y = 3
The two lines when plotted on the graph will give two parallel lines. the graph is been plotted below in image(A).
therefore, the system of equations has no solution.
B.) 2y = 3 – 4x, x+y = 0
The two lines when plotted on the graph will give a point of intersection. the graph is been plotted below in image(B)
therefore, the system of equations has a unique solution.
C.) 12x+2 = 4y – 10, 2x+y = –11
The two lines when plotted on the graph will give a point of intersection. the graph is been plotted below in image(C)
therefore, the system of equations has a unique solution.
D.) –3x – y = 5, 15x = 10 – 5y
The two lines when plotted on the graph will give two parallel lines. the graph is been plotted below in image(D).
therefore, the system of equations has no solution.
E.) x+y = 1, –4x+2y = 7
The two lines when plotted on the graph will give a point of intersection. the graph is been plotted below in image(E)
therefore, the system of equations has a unique solution.
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