Bell Work Systems Elimination/Substitution

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 set of values that satisfy all equations simultaneously.

Front

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

Back

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

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the first step in solving the system 5x + 3y = 7 and y = 4?

Back

Substitute y = 4 into the first equation to find the value of x.

Front

How do you determine which variable to eliminate in a system of equations?

Back

Choose the variable that can be easily eliminated by adding or subtracting the equations, often based on coefficients.

Front

What is the combined equation for the system 9x + y = 12 and -9x + y = 6?

Back

The combined equation is 2y = 18.

Front

What is the solution to the system 4x + 8y = 20 and -4x + 2y = -30?

Back

The solution is (7, -1).

Front

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and do not intersect.

Front

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

Back

It means the equations represent the same line, and every point on that line is a solution.

Front

How can 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.