8-7.4 2024-25 Solving Systems by Elimination

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

One solution: lines intersect at one point; no solution: lines are parallel; infinitely many solutions: lines coincide.

Front

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

Back

The lines representing each equation on a coordinate plane, where their intersection represents the solution.

Front

Solve the system of equations: 5x - 3y = -36 and 2x + 3y = 15.

Back

(-3, 7)

Front

Where do the lines x - y = 11 and 2x + y = 19 intersect?

Back

(10, -1)

Front

Solve the system of equations: 3x + y = -21 and x + y = -5.

Back

(-8, 3)

Front

Solve the system of linear equations: -2x - 10y = 22 and 2x + 5y = -12.

Back

(-1, -2)

Front

Solve the system of equations: 3x + y = -14 and -2x - y = 9.

Back

(-5, 1)