Systems of Equations - Elimination/Substitution

Front

What is a system of equations?

Back

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

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?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

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 are the same.

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 do you convert standard form to slope-intercept form?

Back

Rearrange the equation Ax + By = C to solve for y.

Front

What is the first step in using elimination with the equations 2x + 2y = -2 and 3x - 2y = 12?

Back

You can eliminate one variable by making the coefficients of y the same.

Front

Solve the system using elimination: 4x + 4y = 4 and 3x + 4y = 10.

Back

(-6, 7) is the solution.

Front

Solve the system using substitution: y = 8x + 1 and y = 6x + 3.

Back

(1, 9) is the solution.