Question

a system of equations that has exactly one solution is called ____. a system of equations that has no solutions is called __. a system of equations that has infinite solutions is called __. the graph of a linear equation is a __. to solve a system of equations using substitution, first solve one equation for one __. in the elimination method, you may need to ____ one or both equations to align coefficients.

Explanation:

Sub - question 1:

In the context of systems of linear equations, a system with exactly one solution is called consistent and independent. This is because the equations represent lines (in 2D) that intersect at exactly one point, so there is a unique solution.

A system of equations with no solutions is called inconsistent. For linear systems, this means the lines (in 2D) are parallel and never intersect, so there's no common solution.

A system of equations with infinite solutions is called consistent and dependent. In linear systems, this occurs when the equations represent the same line (in 2D), so every point on the line is a solution.

Answer:

consistent and independent

Sub - question 2: