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Systems of Equations
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Using substitution with Systems of Equations Algebra 1
Key Concepts:
Terms in this set (22)
Parallel Lines
NO SOLUTION
Intersecting Lines
One solution
Same Line
Infinitely many solutions
Substitution
An algebraic model that can be used by substituting the formula of a known variable into the other equation to find the exact solution of a system of equations.
Elimination
An algebraic model that uses eliminating one variable in order to solve for the other variable to find the exact solution of a system of equations.
Substitution
y = 2x + 6
x + y = 18
x + (2x +6) = 18
3x + 6 = 18
3x = 12
x = 4
Plug in x:
y = 2(4) + 6
y = 14
Solution set: (4, 14)
Substitution
2y = 2x + 6
x = 4y
x is already solved
2y = 2(4y) + 6
2y = 8y + 6
-6y = 6
y = -1
Plug the y-value in to the x solved equation
x = 4(-1)
x = -4
Solution set: (-4, -1)
Substitution
2x - 3y = -1
y = x - 1
y is already solved
2x - 3(x - 1) = -1 Be careful with distribution
2x - 3x + 3 = -1 Combine Like Terms
-1x + 3 = -1
-1x = -4
x = 4
Now, plug in the x value to find y (using the solved y equation is easiest)
y = 4 - 1
y = 3
Solution set: (4, 3)
Isolate and substitute
-7x - 2y = -13
x - 2y = 11
None of them are solved for a variable.
Which one is easier? Equation 2 and solve for x
x - 2y = 11
x = 2y + 11
Now, plug in this value FOR x THIS TIME
-7(2y + 11) -2y = -13 Notice the new equations always have the same variable
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = -64
y = 4
Now, plug in the y value and find x
x - 2(4) = 11
x - 8 = 11
x = 19
Solution set: (19, 4)
Substitution
y = 6x - 11
-2x - 3y = -7
Solution set: (2, 1)
Substitution
2x - 3y = -1
y = x - 1
Solution set: (4, 3)
Substitution
y = -3x + 5
5x - 4y = -3
Solution set: (1, 2)
Substitution
-3x - 3y = 3
y = -5x -17
Solution set: (-4, 3)
Substitution
y = -2
4x - 3y = 18
Solution set: (3, -2)
Isolate and Substitution
-4x + y = 6
-5x - y = 21
Solution set: (-3, -6)
Substitution
y = 5x - 7
-3x - 2y = -12
Solution set: (2, 3)
Isolate and substitution
-5x + y = -2
-3x + 6y = -12
Solution set: (0, -2)
Elimination
x + 3y = 1
-3x - 3y = -15
Solution set: (7, -2)
Elimination
-3x + 3y = 4
-x + y = 3
Solution set: No Solution
The result is a false statement
Elimination
6x + 6y = -6
5x + y = -13
Solution set: (-3, 2)
Elimination
-3x - 4y = 2
3x + 3y = -3
Solution set: (-2, 1)
Substitution
-16x + 2y = -2
y = 8x - 1
Solution set: Infinitely many solutions
The result is a true statement
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