Review: Writing & Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that can be solved together.

Front

What does the solution of a system of equations represent graphically?

Back

The point of intersection of the lines represented by the equations.

Front

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

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

Write the system of equations for: 'Two numbers have a sum of 25, and one number is five more than the other.'

Back

x + y = 25, x = y + 5.

Front

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

Back

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

Front

How can you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the graphical representation of the equation y = 2x + 3?

Back

A straight line with a slope of 2 and a y-intercept of 3.

Front

What does it mean for two lines to be perpendicular?

Back

Their slopes are negative reciprocals of each other.

Front

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

Back

Set x = 0 in the equation and solve for y.