## anonymous one year ago PLZ HELP Equation A: y = x + 1 Equation B: y = 4x + 5 Which of the following steps can be used to find the solution to the set of equations? x + 1 = 4x + 5 x = 4x + 5 x + 1 = 4x x + 5 = 4x + 1

1. anonymous

@JoannaBlackwelder

2. JoannaBlackwelder

Any thoughts?

3. anonymous

not really I'm so confused

4. JoannaBlackwelder

Ok, they are using the method of substitution.

5. anonymous

ok

6. JoannaBlackwelder

That is where you solve for a variable and plug it into that variable in the other equation.

7. JoannaBlackwelder

Both of these equations are already solved for y.

8. JoannaBlackwelder

So, we can take what y= in one equation, and plug it in for y in the other equation.

9. JoannaBlackwelder

|dw:1440003635482:dw|

10. anonymous

i thought y = 4x

11. JoannaBlackwelder

I'm not sure what you mean.

12. anonymous

in equation b

13. anonymous

or is that just the slope formula

14. JoannaBlackwelder

Equation b is close to the slope formula, y=mx+b, but it has an x instead of y.

15. anonymous

ok

16. JoannaBlackwelder

But have you followed what I have said so far?

17. anonymous

yes

18. JoannaBlackwelder

So, if you plug in x+1 for y in the second equation, what do you get?

19. anonymous

y=4x+6?

20. JoannaBlackwelder

Hm, no, if we are subbing x+1 in for y, then we don't have y anymore.|dw:1440004062537:dw|

21. anonymous

oh

22. JoannaBlackwelder

:-) Does that make sense?

23. anonymous

yep

24. JoannaBlackwelder

Cool, so what is the answer?

25. anonymous

a

26. JoannaBlackwelder

Yep!

27. anonymous

can u do another plz?

28. anonymous

;)

29. JoannaBlackwelder

Sure

30. anonymous

Equation C: y = 6x + 9 Equation D: y = 6x + 2 Which of the following options is true about the solution to the given set of equations? One solution No solution Two solutions Infinite solutions

31. JoannaBlackwelder

Ok, well, let's see what happens if we do the same thing as the last problem.

32. JoannaBlackwelder

What do you get when you sub 6x+9 for y in the second equation?

33. anonymous

6x+9=6x+2?

34. JoannaBlackwelder

Sweet! Can you simplify that?

35. anonymous

combine like terms?

36. JoannaBlackwelder

Yep

37. anonymous

12x+9=+2??

38. anonymous

@JoannaBlackwelder

39. JoannaBlackwelder

No, to move one 6x to the other side, we need to subtract it

40. JoannaBlackwelder

|dw:1440004496684:dw|

41. anonymous

ohhhh i get it

42. anonymous

so theres only one solution?

43. JoannaBlackwelder

Sweet! So, any thoughts of what that tells us?

44. JoannaBlackwelder

Hm, no. When the two equations simplify to a false statement (9 does not equal 2),

45. JoannaBlackwelder

That means no solution

46. anonymous

ohh

47. JoannaBlackwelder

We can graph them to show that too.

48. JoannaBlackwelder

They have the same slope, but different y intercepts

49. JoannaBlackwelder

So they are parallel lines, and will never cross.

50. JoannaBlackwelder

The solution is the point where the two lines cross.

51. anonymous

one more??

52. JoannaBlackwelder

Sure :-)

53. anonymous

y = 3x + 4 2x + 3y = 10 Which of the following steps could be used to solve by substitution? 3x + 4 = 2x + 3y 2x + 3(3x + 4) = 10 2(3x + 4) + 3y = 10 3(y = 3x + 4)

54. JoannaBlackwelder

Ok, any thoughts?

55. anonymous

no

56. JoannaBlackwelder

The first equation is solved for y.

57. JoannaBlackwelder

So, we take what y is in terms of x, and plug it into the other equation.

58. JoannaBlackwelder

Can you try to do that?

59. anonymous

im lost, ugh and my online teacher keeps reminding me about time crunch lol

60. JoannaBlackwelder

|dw:1440004939079:dw| Aw, that's frustrating!

61. anonymous

i see

62. JoannaBlackwelder

It is like the other ones, just the second equation isn't solved for y.

63. anonymous

ho do i slove

64. anonymous

how

65. JoannaBlackwelder

We aren't supposed to solve, just substitute.

66. anonymous

ok

67. JoannaBlackwelder

|dw:1440005055460:dw|

68. JoannaBlackwelder

See how I subbed the 3x+4 in for y in the second equation?

69. anonymous

yes

70. JoannaBlackwelder

That is all we have to do :-)

71. JoannaBlackwelder

Which answer does that look like?

72. anonymous

b

73. JoannaBlackwelder

Right

74. anonymous

one more, last one i promise lol

75. JoannaBlackwelder

Haha, ok

76. anonymous

d + e = 15 −d + e = −5 Label the ordered pair as (d, e). (0, 0) (10, −5) (5, 10) (10, 5)

77. JoannaBlackwelder

Ok, this one we actually do have to solve. Any thoughts on how to start?

78. anonymous

not really

79. JoannaBlackwelder

Well, what happens when we add the two equations together?

80. anonymous

we sub?

81. JoannaBlackwelder

We could, but we would have to solve for one of the variables first.

82. anonymous

ok

83. JoannaBlackwelder

I would suggest to use elimination on this one. It is the easier method. :-)

84. anonymous

ok

85. JoannaBlackwelder

|dw:1440005374033:dw| What happens when we add the two equations together?

86. anonymous

im not sure

87. JoannaBlackwelder

Just take a guess

88. anonymous

elimintion

89. JoannaBlackwelder

Ok, but what equation are we left with?

90. anonymous

i honestly don't know

91. JoannaBlackwelder

|dw:1440005536799:dw| See how I added the equations together?

92. anonymous

yes

93. JoannaBlackwelder

Can you combine like terms?

94. anonymous

ill be back in one min, my teacher is calling me

95. JoannaBlackwelder

Ok

96. anonymous

I'm back @JoannaBlackwelder

97. JoannaBlackwelder

Ok, can you combine like terms?

98. anonymous

that one is kinda hard

99. JoannaBlackwelder

It is a little different. d-d is what?

100. anonymous

d

101. JoannaBlackwelder

No, it is like 2-2.

102. anonymous

0

103. JoannaBlackwelder

Right. :-)

104. JoannaBlackwelder

And e+e is what?

105. anonymous

e

106. JoannaBlackwelder

No, we add the coefficients, and when there is no coefficient written it is understood to be 1. So this is 1e+1e

107. anonymous

2

108. JoannaBlackwelder

Close, 2e

109. anonymous

oh i see

110. JoannaBlackwelder

:-) And what is 15-5?

111. anonymous

10

112. JoannaBlackwelder

|dw:1440006758146:dw| Great!

113. JoannaBlackwelder

See how I simplified that?

114. anonymous

yep

115. JoannaBlackwelder

Sweet, so we need to finish getting e by itself.

116. JoannaBlackwelder

It is currently multiplied by 2

117. JoannaBlackwelder

So, we need to divide the left side by 2 to leave just e (or 1e)

118. anonymous

|dw:1440006877761:dw|

119. JoannaBlackwelder

Good effort! But we need to divide by 2 to get e by itself, not 10

120. anonymous

ok

121. JoannaBlackwelder

|dw:1440006917075:dw|

122. anonymous

ok

123. anonymous

so whats my second point

124. JoannaBlackwelder

Well, now that we know that e is 5, which answers do we have to choose from?

125. anonymous

c,d

126. anonymous

?

127. JoannaBlackwelder

Are you sure that both c and d have e being 5?

128. anonymous

c?

129. JoannaBlackwelder

No, c, has e as 10.

130. anonymous

d

131. JoannaBlackwelder

Yep, that is the only answer that has e as 5. We would normally also have to find d, but they gave us a shortcut. :-)

132. anonymous

thank u

133. JoannaBlackwelder

You're welcome