Systems of Linear Equations Review

Front

What is a system of two identical (overlapping) lines?

Back

A system of two identical (overlapping) lines has infinite solutions because every point on the line is a solution.

Front

Write a system of equations for the following situation: Two groups of people order food at a restaurant. One group orders 4 pizzas and 7 salads for $34.50. The other group orders 8 pizzas and 3 salads for $30.50.

Back

4p + 7s = 34.50 and 8p + 3s = 30.50

Front

If a system of linear equations has infinitely many solutions, what does this mean about the two lines?

Back

The two lines are the same line.

Front

If a system of linear equations has 1 solution, the solution is the ____________ of intersection.

Back

point

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Front

What does it mean if two lines are parallel in a system of linear equations?

Back

It means there is no solution to the system because the lines never intersect.

Front

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

Back

If the lines are parallel, the system has no solution.

Front

What is the graphical representation of a system of linear equations?

Back

The graphical representation is the intersection points of the lines on a coordinate plane.

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 point of intersection of two lines algebraically?

Back

Set the equations equal to each other and solve for x, then substitute back to find y.