Algebra 1:Topic 4 (Systems of Linear Equations & Inequalities)

Front

What does a solid line represent in a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set (≥ or ≤).

Front

What is the solution to the system of equations y = -4x + 5 and y = 3x - 16?

Back

(3, -7)

Front

If nachos cost $1.50 each and sodas cost $0.50 each, how many nachos and sodas did David sell if he made a total of $78.50 from 87 items?

Back

35 nachos and 52 sodas.

Front

What does the symbol '≥' mean in an inequality?

Back

It means 'greater than or equal to'.

Front

How do you solve a system of equations by substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation shows equality (e.g., y = mx + b), while a linear inequality shows a range of values (e.g., y < mx + b).

Front

What does the solution (x, y) represent in a system of linear equations?

Back

It represents the point where the two lines intersect, indicating the values of x and y that satisfy both equations.

Front

What is the graphical representation of the inequality y ≤ 2/5x + 1?

Back

A shaded region below the line y = 2/5x + 1, including the line itself.

Front

What is the first step in solving the system of equations by substitution?

Back

Isolate one variable in one of the equations.

Front

What does it mean if a line is dashed in a graph of a linear inequality?

Back

It means that the points on the line are not included in the solution set (< or >).