Solving Equations & Systems

One-Step Equations

3

3 = -2 – x

x= -5

4

5x = -80

x= 16

5

-16 = x+2

x= -18

Two-Step Equations

1

6x – 13 = 11

x= 4

2

3x + 5 = 14

x= 3

3

(x/2) =-8

x= -16

4

(x/2)=10

x= 20

5

(x/3)=-3

x= -9

Mixed Equations

2

Solving Equations

-5p + 1 = 6

p = -1

3

Solving Equations

2n+10 = 4

n = -3

4

Solving Equations

5(m-3) = 4

m = 19/5

5

Solving Equations

3(𝑥 − 9) = −3

x = 8

Multi-Step Equations

2

Solving Equations

5 + 5x - 1 = 29

x = 5

3

Solving Equations

-45 = 3x + 4 + 4x

x = -7

4

Solving Equations

14 = -(2a + 6) + 2

a= -9

5

Solving Equations

-21 = 7(5k - 8)

k = 1

Equations with Variables on Both Sides

1

4x - 2 = 3x + 5

x = 7

2

2(x - 4) = 5x + 4

x = -4

3

6x + 3 - 2x = 2x + 11

x = 4

4

9 - x = 6 + 2x

x = 1

5

6x - 15 + 4x = 5(2x - 3)

ALL REAL NUMBERS

Systems

1

Define the word system. Give one real-life example of a system.

A group of independent, connected parts that work together to form a unified whole

A set of equations with the same variables

Examples may vary

2

Systems that each have the same slope but different y-intercepts are which type of line? Parallel, Coinciding (on top of each other) or Intersecting?

Parallel

3

What is the solution to a system of equations?

Where the lines INTERSECT.

or

When the equations have the same x & y.

4

How many solutions would this system have? 

y=3x+5

y=3x+5

An infinite number of solutions

5

What is substitution?

How do we use it to solve a system of equations?

Replacement!

We isolate one variable then REPLACE it!