Systems of Equations - elimination

Solve using a matrix: -8x - 10y = 20 and -8x - 6y = -4.

• (5, -6)

• (2, 3)

• (0, -4)

• (-1, 1)

What is a system of equations?

• A single equation with multiple variables.

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

• An equation that has no solution.

• A method for solving quadratic equations.

What does it mean to solve a system of equations?

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

• Identifying the number of equations in the system.

• Graphing the equations to find their intersection points.

• Eliminating one variable to simplify the equations.

What does it mean if a system of equations has an infinite number of solutions?

• The equations represent different lines that intersect at one point.

• The equations represent the same line, meaning every point on the line is a solution.

• The equations have no solutions, meaning they are parallel lines.

• The equations represent two distinct lines that intersect at multiple points.

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

• The equations represent parallel lines that never intersect.

• The equations have exactly one point of intersection.

• The equations represent the same line.

• The equations have infinitely many solutions.

A farm has 20 animals in all. There are pigs and chickens running all around. There are a total of 78 legs on the farm. How many of each animal are there?

• 18 pigs and 2 chickens

• 19 pigs and 1 chicken

• 20 pigs and 0 chickens

• 15 pigs and 5 chickens

Solve using a matrix: 3x + 2y = –13 and 3x + 4y = 1.

• (-9, 7)

• (0, -7)

• (1, -5)

• (-3, 4)

What is the graphical representation of a system of equations?

• The points where the graphs of the equations intersect represent the solutions.

• The area under the curve of the equations represents the solutions.

• The slope of the equations indicates the solutions.

• The distance between the lines represents the solutions.

A farm has 20 animals on it. There are pigs and chickens all over the place. There are 70 legs in all. How many of each animal are there?

• 10 pigs and 10 chickens

• 15 pigs and 5 chickens

• 20 pigs and 0 chickens

• 5 pigs and 15 chickens

Solve using a matrix: -4x + 9y = 9 and x - 3y = -6.

• (9, 5)

• (1, 2)

• (0, 0)

• (-3, 4)