5C/2I Write and Solve Systems STAAR Review

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by substitution?

Back

To solve by substitution, you solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation shows the lines of the equations on a coordinate plane. The point(s) where they intersect represent the solution(s).

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.

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What does it mean if a system of equations has infinitely many solutions?

Back

Infinitely many solutions occur when the equations represent the same line, meaning every point on the line is a solution.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the purpose of the setup fee in a cost equation?

Back

The setup fee is a fixed cost that must be paid regardless of the number of items purchased, affecting the total cost.

Front

How can you represent a real-world problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described, and ensure they reflect the problem's constraints.

Front

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

Back

The first step is to rewrite each equation in slope-intercept form (y = mx + b) if necessary.