Solving Systems of Equations

Vocabulary

100

The point where two lines cross.

What is the intercept/intersect

200

This is where you plot points of two lines to see where the two lines cross.

What is Solving by Graphing.

300

Where you replace the variable in one equation with an expression from another equation.

What is solving by substitution.

400

When you solve a system of equations, your answer is a ...

A point, no solution, or infinite solutions

500

What is system of linear equations ?

Two equations

Solving by Graphing

100

Solve by graphing: y = x - 3 y = -x - 1

solution is (1,-2)

200

Solve by graphing: y = -2x - 1 y = x + 5

Solution is ( -2,3)

300

Solve by graphing: y = 1/3x - 3, y = 4 - 2x

Solution is (3,-2)

400

Lawn Care charges $30 per bag of mulch and a $30 delivery fee. Yard Depot charges $25 per bag of mulch and $55 for a delivery fee. At what number of bags is the cost the same?

Solution is 5 bags, $180.

500

Anthony has $7 saved up and saves $1 more each week. Marc has $4 saved up and saves $2 more each week. When will they have the same amount saved up?

Solution is 3 weeks, $10

Solving by Substitution

100

Solve by substitution: y = 2x, y = x + 5

Solution is (5, 10)

200

Solve by substitution: 2x + y = 5, y = x - 4

Solution is (3,-1)

300

Solve by substitution: y = x + 3, y = 2x + 5

Solution is (-2, 1)

400

Solve by substitution: x = 2y - 4, x + 8y = 16

Solution is (0, 2)

500

Solve by substitution: 2x + y = -4, x = -7 - y

Solution is (3, -10)

Knowledge

100

In solving by graphing, how many lines do you need to graph?

At least two.

200

How many variables should be in your equation after you substitute for one of them?

One

300

Is (4,1) a solution of: x + 2y = 6, x - y = 3

Yes, (4) + 2(1) = 6 (4) - (1) = 3

400

When you solve a system of equations by substitution, how many time do you substitute?

Twice

500

Is (1,3) a solution of: 2x + y = 5, -2x + y = 4

No, 2(1) + (3) = 5 but -2(1) + 3 = 1, not 4

Random

100

This is how you know whether a system has no solution.

What is they have the same slope/ are parallel lines.

200

How many solutions does a perpendicular set of lines have?

What is one.

300

Solve: 8x+y = 27 and -3x+4y = 3

What is (3,3)

400

Solve: 6x - 4y = 30 and 12x + 5y = -18

What is (1,-6)

500

At an office supply store, Emilio bought 3 notebooks and 5 pens for $13.75. If a notebook costs $1.25 more than a pen, how much does one notebook cost?

What is $2.50