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Grade 10 Linear Systems
9
- Find the point of intersection (P.O.I)
- This P.O.I is the solution
- The solution is (2,0)
Graph the two equations on the same coordinate system
Add (1) with (2), and solve for "x"
(1) 6x + 2y = 20
+(2) -4x - 2y = 2
2x + 0y = 22
x = 11
Solve for "y"
-4x - 2y = 2
-4(11) - 2y = 2
y = -23
Remember to check with the other equation!!
6x + 2y = 20
6(11) + 2 (-23) = 20
20 = 20
Therefore x = 11 and y = -23
For example:
(1) 3x + y = 10
(2) -4x − 2y = 2
We will eliminate "y" by multiplying the first equation by "2"
(1) 6x + 2y = 20
(2) -4x - 2y = 2
Notice the coefficients in front of "y" are the same just opposite signs
Graphing
- graph both equations in the same coordinate system
- solution is the point where the two lines intersect
- this point is known as the point of intersection
Elimination
- Choose a variable to eliminate
- Line the equations one on top of the other
- Ensure the coefficients of the variable you are eliminating are the opposites
- Add the two equations
- Solve for the variable that was not eliminated
- Substitute the answer to solve for the other variable
- Check you solution
Linear Systems
- contains two or more linear equations
- solution of such a system is the ordered pair that is a solution to both equations
- can solve by graphing, substitution or elimination
Substitution
- solve/rearrage one of the equations (you choose which one) for one of the variables (you choose which one)
- plug this into the other equation, "substituting" for the chosen variable and solving for the other
- by using this value, solve for the other variable
- check using the other equation
System of Equations
For example:
(1) 2y = -6x + 12
(2) y = 2x - 4
Rearrange (1) as
y = -3x + 6
substitute equation (1) into equation (2)
-3x + 6 = 2x - 4
solve for the x
-3x + 6 = 2x - 4
-3x - 2x = - 4 - 6
- 5x = -10
x = 2
Use x = 2 to solve for y
y = -3x + 6
y = -3(2) + 6
y = 0
Remember to check using the other equation !!
y = 2x - 4
0 = 2(2) - 4
0 = 0
Therefore x = 2 and y = 0