A system of two linear equations is shown.
5x + 2y = –4
5x + 2y = 1
Which statement is true regarding the solution to this system of linear equations?
A.The system has no solution.
B.The system has one unique solution at (5, 2).
C. The system has one unique solution at (–4, 1).
D. The system has an infinite number of solutions.
Answers
5x + 2y = 1
0=5
A. No solution
We need to find which of the given statements are true.
The system of linear equations has no solutions.
First let us find what type of solution does the system have
The equations are
[tex]5x+2y=-4[/tex]
[tex]5x+2y=1[/tex]
So,
[tex]\dfrac{a_1}{a_2}=\dfrac{5}{5}=1[/tex]
[tex]\dfrac{b_1}{b_2}=\dfrac{2}{2}=1[/tex]
[tex]\dfrac{c_1}{c_2}=\dfrac{-4}{1}=-4[/tex]
So,
[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]
This means the two lines do not intersect and are parallel.
Hence, the system of linear equations has no solutions.
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