Solving Systems of Linear Equations by Graphing and Substitution
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| What is the solution to the following system of linear equations: * Line 1: y=3x – 1 * Line 2: y= x – 5 | Set the Two Equations Equal to each other then solve for x
1) Substitute the x value, -2, into either equation to determine y coordinate of solution
2) y=(-2) - 5 or -7
3) The solution is the point (-2, -7)
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| Set the two equations equal to calculate the solution to the system below: * Line 1: y= x + 1 * Line 2: y= 2x | y= x + 1 and y= 2x
x+1 = 2x
-x -x
1=x
y=2(1)
y=2
solution= (1,2)
The solution of this system is the point of intersection : (1,2)
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| Solve the following system of linear equations by graphing. * 2y = 4x + 2 * and 2y = -x + 7 | * 2y = 4x + 2
o ½(2y) = ½(4x + 2)
o y = 2x +1
* 2y = 8x - 2
o ½(2y) = ½(8x - 2)
o y = 4x – 1
the solution of the point is (1,3)
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| Solve the following system by substitution. y = 36 – 9x 3x + y/3 = 12 | 3x + (36 – 9x)/3 = 12
3x + 12 – 3x = 12
12 = 12
solution: y = 36 – 9x
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| solve for one variable. 6x + 2y = 9 and 4x + y - 5 = 10. | 6x + 2y = 9 ,4x + y - 5 = 10
[ - 4x] 4x + y - 5 = 10 [ - 4x]
y - 5 [ + 5] = 10 - 4x + 5
y = 10 - 4x + 5
6x + 2y = 9
6x +2(10 - 4x + 5) = 9
6x + 20 - 8x +10 = 9
[ - 30] -2x + 30 = 9 [ - 30]
- 2x = - 21
x = 10.5
y = - 27
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| solve this system of equations and check. y - 2x = 11 y + 2x = 9 | 3y - 2x = 11
y = 9 - 2x
3(9 - 2x) - 2x = 11
(27 - 6x) - 2x = 11
27 - 6x - 2x = 11
27 - 8x = 11
-8x = -16
x =2
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| Solve the following system: x + y = 11 3x - y = 5 | Now, substitute 11 - x for y
in the second equation
3x - (11 - x) = 5
3x - 11 + x = 5
4x = 16
x = 4
Now, substitute 4 for x
4 + y = 11
y = 7
(4, 7)
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| Example: Which of the ordered pairs in the set {(5, 4),(3, 8),(6, 4),(4, 6),(7, 2)} is a solution of the following system of equations: y + 2x = 14 xy = 24 | (5, 4) is a solution of the first equation.
(3, 8) is a solution of both equations.
(6, 4) is a solution of the second equation.
(4, 6) is a solution of both equations.
(7, 2) is not a solution.
The solution set of the system is {(3, 8),(4,
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