A system of linear equations consists of two or more linear equations with two or more variables. The solution to a system is the point where the lines intersect. A system can have 1) one solution, 2) no solution, or 3) infinite solutions. There are three methods to solve a system of linear equations: 1) graphing, 2) elimination, and 3) substitution. The elimination method removes a variable by adding or subtracting the equations while the substitution method replaces a variable in one equation with an expression containing that variable from the other equation.

1. System of Linear
Equations
MYP 10 ­ CIC

2. 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

3. What is the solution of a system
of linear equations?
The solution is where the equations meet
or intersect.

4. How many solutions can a system
of linear equations have?
Case 1: 1 solution

5. How many solutions can a system
of linear equations have?
Case 2: no solution

6. How many solutions can a system
of linear equations have?
Case 3: infinite solutions

7. How can we find solutions to the
system of equations?
1) Solve by graphing
2) Solve by elimination
3) Solve by substitution

8. Elimination Method
2x – y = 1
3x + y = 9
We have the same number of
y’s in each
If we ADD the equations, the y’s disappear+
5x = 10 Divide both sides by 5
x = 2
A
B
Substitute x = 2 in equation A
2 x 2 – y = 1
4 – y = 1
y = 3
Answer
x = 2, y = 3

9. Substitution Method
2x – y = 1
3x + y = 9
A
B y = −3x + 9
2x −(−3x + 9) =1substitute
2x +3x − 9 =1
5x − 9 =1
5x =10
x = 2
3(2)+ y = 9
6+ y = 9
y = 9 − 6
y = 3

10. Graphing Method
2x – y = 1
3x + y = 9
A
B
2x – 1 = y
y = -3x + 9
(2, 3)

11. Solve
3x - 2y = 7
5x + 3y = 37
+
19x = 95
In B
A
B
5 x 5 + 3y = 37
3y = 12
y = 4 Answer
x = 5, y = 4
Multiply A by 3 & B by 2,
we get +6y & -6y
9x – 6y = 21
10x + 6y = 74B
A
x = 5
Could multiply A by 5 & B
by 3 to get 15x in each

12. Solve

13. Solution:
a)(2, 5)
b)(3, 1)
c)(2, 4/3)
d)(2, -2)
e)(-3, 4)
f)(2, -3)
g)Infinite solutions
h)No solutions