Page 6
Solutions To Linear Equations in Two Variables
Which of the following ordered pairs are solutions to the equation listed above the ordered pairs?
Show your work. Put yes if the ordered pair is a solution and No if it is not a solution.
1.
!
A.
y = 3x + 4
x
y
(−3 ,−5)
!
B.
x
y
(0, 4)
(−3,−5) means x = −3 means y = −5
substitute x = −3 and y = −5
into y = 3x + 4 and see if the equation is true.
( 0 , 4) means x = 0 means y = 4
substitute x = 0 and y = 4
into y = 3x + 4 and see if the equation is true.
−5 = 3(−3) + 4
−5 = −9 + 4
−5 = −5
TRUE
4 = 3(0) + 4
4=0+4
4=4
TRUE
!
YES
(−3,−5) is a solution to y = 3x + 4
YES
(0,4) is a solution to y = 3x + 4
!
C.
!
x y
(−1 ,1 )
(−1 , 1) means x = −1 means y = 1
substitute x = −1 and y = 1
into y = 3x + 4 and see if the equation is true.
1 = 3(−1) + 4
1 = −3 + 4
1=1
TRUE
YES
(−1,1) is a solution to y = 3x + 4
Math 30 !
Chapter 10 pages 6 and 7!
© 2016 Eitel
page 6 continued
2.
!
A.
y = −2x − 5
x y
(−1 ,7)
!
B.
x
y
( 2 , −9 )
(−1,7) means x = −1 means y = 7
substitute x = −1 and y = 7
into y = −2x − 5 and see if the equation is true.
(2,−9) means x = 2 means y = −9
substitute x = 2 and y = −9
into y = −2x − 5 and see if the equation is true.
7 = −2(−1) − 5
7= 2−5
7 = −3
FALSE
−9 = −2(2) − 5
−9 = −4 − 5
−9 = −9
TRUE
!
NO
(−1,7) is NOT a solution to y = −2x − 5
!
C.
YES
(2,−9) is a solution to y = −2x − 5
!
x
y
(0 ,−5 )
(0,−5) means x = 0 means y = −5
substitute x = 0 and y = −5
into y = −2x − 5 and see if the equation is true.
−5 = 3(0) − 5
−5 = 0 − 5
−5 = −5
TRUE
YES
(0,−4) is a solution to y = −2x − 5
Math 30 !
Chapter 10 pages 6 and 7!
© 2016 Eitel
page 7
6.
!
y=
A.
1
x +1
2
(0 , 1) !
(0,1) means x = 0 means y = 1
substitute x = 0 and y = 1
1
into y = x + 1 and see if the equation is true.
2
1 ⎛ −4 ⎞
+1
2⎝ 1 ⎠
−4
−1 =
+1
2
−1 = −2 + 1
−1 = −1
TRUE
−1 =
1
1 = (0) + 1
2
1= 0 +1
1=1
TRUE
!
YES
(0,1) is a solution to y =
B. (−4 , −1) !
(−4,−1) means x = −4 means y = −1
substitute x = −4 and y = −1
1
into y = x + 1 and see if the equation is true.
2
1
x +1
2
YES
(−4,−1) is a solution to y =
1
x +1
2
C. (6 , 4 ) !
(6,4) means x = 6 means y = 4
substitute x = 6 and y = 4
1
into y = x + 1 and see if the equation is true.
2
1 ⎛ 6⎞
+1
2 ⎝ 1⎠
12
4=
+1
2
4 = 3 +1
4=4
TRUE
4=
YES
(6,4) is a solution to y =
Math 30 !
1
x +1
2
Chapter 10 pages 6 and 7!
© 2016 Eitel
page 7 continued
2
7. y = x − 4
3
!
A. (6 , 5) !
B.
(6,5) means x = 6 and y = 5
substitute x = 6 and y = 5
2
into y = x − 4 and see if the equation is true.
3
(−3,−6) means x = −3 means y = −6
substitute x = −3 and y = −6
1
into y = x + 1 and see if the equation is true.
2
2
5 = (6) − 4
3
12
5= −4
3
5= 4−4
5=0
FALSE
−6 =
!
2
(−3) − 4
3
−6
−6 =
−4
3
−6 = −2 − 4
−6 = −4
TRUE
YES
NO
(6,5) is NOT a solution to y =
C.
(−3 , − 6) !
2
x−4
3
(−3,−6) is a solution to y =
2
x−4
3
(0 , − 4) !
(0,−4) means x = 0 means y = −4
substitute x = 0 and y = −4
1
into y = x + 1 and see if the equation is true.
2
2
(0) − 4
3
−4 = 0 − 4
−4 = −4
TRUE
−4 =
YES
(0,−4) is a solution to y =
Math 30 !
2
x−4
3
Chapter 10 pages 6 and 7!
© 2016 Eitel
Math 30 !
Chapter 10 pages 6 and 7!
© 2016 Eitel