A system of two linear equations in two variables has infinitely many solutions when which condition is satisfied?
A$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$
B$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$
C$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
D$a_1a_2+b_1b_2=c_1c_2$
Answer & Solution
Correct answer: C. $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
A pair of linear equations has infinitely many solutions when the two equations represent the same line. Algebraically, this happens when the ratios of corresponding coefficients and constants are all equal: $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$. Option B instead gives no solution, because the lines are parallel but distinct.
Related questions
The study of inequalities is described as useful in solving problems in science and:A firm needing at least 6 units and at most 10 would write that as a:Which sign makes a statement an inequality rather than an equation?Unless stated otherwise, inequalities in that chapter are solved over the set of:The set of all values of the variable that make an inequality true is called its:Solving 4x plus 3 less than 6x plus 7 gives:When x is a real number in that inequality, the solution set is written as:When x is an integer in that inequality, the largest solution is: