Solving Systems of Equations 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 of equations by elimination?

Back

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

Front

What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by combining the equations to eliminate one variable.

Front

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

Back

If the lines intersect at one point, there is one solution. If the lines are parallel, there is no solution. If the lines coincide, there are infinitely many solutions.

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 the coefficients of one variable are opposites.

Front

Solve the system: {x - 2y = 10, x + 3y = 5}

Back

(8, -1)

Front

Solve the system: {3x = 2y - 7, 2x - 5y = 10}

Back

(-5, -4)

Front

Solve the system: {3x - 4y = -14, 3x + 2y = -2}

Back

(-2, 2)

Front

At a baseball game, Henry bought 5 hotdogs and 3 bags of chips for $14.82. Scott brought 7 hotdogs and 6 bags of chips for $22.89. Find the cost of each hotdog and bag of chips.

Back

$2.25 hotdogs, $1.19 chips

Front

Solve the system: {x + 3y = 5, x = -6y + 14}

Back

(-4, 3)