Which mathematical topic is best tested by the system 2x-3y=7 and 4x+y=5?

Which mathematical topic is best tested by the system 2x-3y=7 and 4x+y=5?

• A. Solving a system of linear equations
• B. Factoring polynomials
• C. Analyzing geometric proofs
• D. Calculating derivatives

Answer: (A)

When two linear equations share the same variables, you're looking for the pair of values that makes both equations true at once. Each equation represents a line on the coordinate plane, and solving the system means finding their intersection point—the values of x and y that satisfy both lines simultaneously. These equations are linear in x and y, so standard methods like substitution or elimination will lead to that unique intersection (or show there isn’t one, or that there are infinitely many if the lines coincide). For example, solving these two equations by substitution gives x = 11/7 and y = -9/7, confirming a single intersection point. Other options refer to different areas: factoring polynomials is about one-variable algebra, geometric proofs concern proving statements about shapes, and derivatives belong to calculus.

When two linear equations share the same variables, you're looking for the pair of values that makes both equations true at once. Each equation represents a line on the coordinate plane, and solving the system means finding their intersection point—the values of x and y that satisfy both lines simultaneously. These equations are linear in x and y, so standard methods like substitution or elimination will lead to that unique intersection (or show there isn’t one, or that there are infinitely many if the lines coincide). For example, solving these two equations by substitution gives x = 11/7 and y = -9/7, confirming a single intersection point. Other options refer to different areas: factoring polynomials is about one-variable algebra, geometric proofs concern proving statements about shapes, and derivatives belong to calculus.