Module 5 - Solving Systems of Linear Equations by Graphing and Substitution
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| A ______ __ ______ ________ consists of two or more linear equations. | system of linear equations
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| Solve by graphing -x+3y=10 x+y=2 | (-1,3)
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| A system of equations that has at least one solution is a _______ ________. | Consistent System
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| A system that has no solution is an _______ ________. | Inconsistent System
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| How many solutions do they have: a)one point of intersection b)parallel lines c)same line | a)one solution
b)no solution
c) infinite number of solutions
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| Solve using the substitution method: 2x+y=10 x=y+2 | 2x+y=10 (first equation)
2(y+2)+y=10 (substitute y+2 for x since x=y=2)
2y+4+y=10( use distributive property)
3y+4y=10 (combine like terms)
3y=6 (subtract 4 from both sides)
y=2 (divide both sides by 3)
x=y+2 (second equation)
x=2+2( let y=2)
x
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| __________ method is a method of solving a system of equations wherein one of the equations is solved for one variable in terms of the other variables. | Substitution
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| Solve using the substitution method: 5x-y =-2 y =3x | 5x-y =-2 (first equation)
5x-(3x)=-2(substitute 3x for y)
2x=-2(combine like terms)
x=-1(Divide both sides by 2)
y=3x(second equation )
y=3(-1)(let x be -1)
y=-3
Solution:(-1,-3)
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| Solve using the substitution method: 6x+12y=5 -4x-8y=0 | -4x-8y=0
-8y=4x
-8y/8=4x/-8
y=1/2x
6x+12y=5
6x+12(-1/2x)=5
6x+(-6x)=5
0=5
no soution
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| Solve using the substitution method: 3y - 2x = 11 y + 2x = 9 | 3y - 2x = 11
3(9 - 2x) - 2x = 11
27 - 6x) - 2x = 11
27 - 6x - 2x = 11
27 - 8x = 11
-8x = -16
x = 2
y = 9 - 2x
y = 9 - 2(2)
y = 9 - 4
y = 5
(2,5)
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