System of Linear Equations

MYP 10 - CIC

What is a system of equation?

A system of equations just means -

more than 1 equation

more than 1 variable (x & y)

more than 1 line

What is the solution of a system of linear equations?

The solution is where the equations meet or intersect.

How many solutions can a system of linear equations

have?

Case 1: 1 solution

How many solutions can a system of linear equations

have?

Case 2: no solution

How many solutions can a system of linear equations

have?

Case 3: infinite solutions

How can we find solutions to the system of equations?

1) Solve by graphing

2) Solve by elimination

3) Solve by substitution

Elimination Method

2x – y = 1

3x + y = 9

We have the same number of y’s in

eachIf we ADD the equations, the y’s disappear+

5x = 10 Divide both sides by 5

x = 2

AB

Substitute x = 2 in equation A

2 x 2 – y = 1

4 – y = 1y = 3

Answerx = 2, y = 3

Substitution Method2x – y = 1

3x + y = 9

A

B

substitute

Graphing Method2x – y = 1

3x + y = 9

A

B

2x – 1 = y

y = -3x + 9

(2, 3)

Solve

3x - 2y = 7

5x + 3y = 37

+19x = 95

In B

AB

5 x 5 + 3y = 373y = 12

y = 4 Answerx = 5, y = 4

Multiply A by 3 & B by 2, we get +6y & -6y

9x – 6y = 2110x + 6y = 74B

A

x = 5

Could multiply A by 5 & Bby 3 to get 15x in each

Solve

Solution:

a)(2, 5)b)(3, 1)c)(2, 4/3)d)(2, -2)e)(-3, 4)f)(2, -3)g)Infinite solutionsh)No solutions