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