Systems of Equations flashcards

Question 1

What is a system of linear equations in two variables?

Accepted Answer

A set of two or more linear equations involving the same variables (often $x$ and $y$). A solution is an ordered pair $(x,y)$ that satisfies every equation in the system.

Question 2

Solve by elimination: $2x+y=8$ and $-2x+3y=4$.

Accepted Answer

Add equations: $(2x+y)+(-2x+3y)=8+4 \Rightarrow 4y=12 \Rightarrow y=3$. Substitute into $2x+y=8$: $2x+3=8 \Rightarrow x=\frac{5}{2}$. Solution: $\left(\frac{5}{2},3\right)$.

Question 3

How do you set up a system of equations from a word problem?

Accepted Answer

Define variables for unknowns, write two independent equations from the relationships given (e.g., totals, rates, or comparisons), then solve the system and interpret the solution with units and context.

Systems of Equations flashcards

Master Math with AI

Learning Resources

Trusted & Recognized