Solving Systems by Elimination

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 by elimination?

Back

Solving a system by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and write them as a system.

Front

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

Back

The first step is to align the equations and manipulate them (if necessary) so that one variable can be eliminated.

Front

If Ride charges $2 for pick up and $2.50 per mile, how would you express the total cost as an equation?

Back

Total cost = 2 + 2.5m, where m is the number of miles.

Front

If Transport charges $2.70 per mile, how would you express the total cost as an equation?

Back

Total cost = 2.7m, where m is the number of miles.

Front

What is the solution to the system of equations 4x + 9y = 28 and -4x - y = -28?

Back

The solution is (7, 0).

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Front

What is the significance of the point where two lines intersect in a system of equations?

Back

The intersection point represents the solution to the system, indicating the values of the variables that satisfy both equations.

Front

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

Back

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