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
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