Exercise · ZW-SYSTEM-OF-LINEAR-EQUATIONS-005 · ★☆☆ Basic
How many solutions does the system \(x+y=1,\; x+y=3\) have?
Choose one option.
Show answer
- A. None
Explanation
If \(x+y\) were 1 and 3 at the same time we would have a contradiction. The lines are parallel and distinct, so the system has no solution (it is inconsistent).
Review the concept: System of linear equations
A system of linear equations is a set of linear equations in the same unknowns. A solution is an assignment of values that satisfies all the equations at once.
\[\begin{aligned}a_{11}x_1+\cdots+a_{1n}x_n&=b_1\\ \vdots\qquad&\\ a_{m1}x_1+\cdots+a_{mn}x_n&=b_m\end{aligned}\]
More practice problems: system of linear equations
- ZW-SYSTEM-OF-LINEAR-EQUATIONS-001 Which of the following equations is linear in the unknowns x and y?
- ZW-SYSTEM-OF-LINEAR-EQUATIONS-002 Solve the system x+y=5,\; x-y=1.
- ZW-SYSTEM-OF-LINEAR-EQUATIONS-003 Which of the following systems has (x,y)=(2,1) as a solution?
- ZW-SYSTEM-OF-LINEAR-EQUATIONS-004 How many solutions does the system x+y=2,\; 2x+2y=4 have?
- ZW-SYSTEM-OF-LINEAR-EQUATIONS-006 For which value of k does the system x+y=1,\; 2x+2y=k have infinitely many solutions?
- ZW-SYSTEM-OF-LINEAR-EQUATIONS-007 Solve the system x+y+z=6,\; x-y+z=2,\; 2x+y-z=1.
- ZW-SYSTEM-OF-LINEAR-EQUATIONS-008 What is the augmented matrix of the system 2x-y=3,\; x+4y=-1?
- ZW-SYSTEM-OF-LINEAR-EQUATIONS-009 For which values of k does the system x+2y=1,\; 3x+ky=2 have a unique solution?
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