Solving Equations Using Substitution Quick Check
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Question
Solve the system of two equations using substitution.
y=2+3x
4x−3y=−16 (1 point)
Responses
(−2, −4)
left parenthesis negative 2 comma negative 4 right parenthesis
(−2, 4)
left parenthesis negative 2 comma 4 right parenthesis
(2, 10)
left parenthesis 2 comma 10 right parenthesis
(2, 8)
17 answers
left parenthesis 2 comma 8 right parenthesis
Solve the system of equations.
2x+6y=−18
x=5y−1 (1 point)
Responses
(−7.25, −1.25)
left parenthesis negative 7.25 comma negative 1.25 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(5.25, 1.25)
left parenthesis 5.25 comma 1.25 right parenthesis
(−6, −1)
2x+6y=−18
x=5y−1 (1 point)
Responses
(−7.25, −1.25)
left parenthesis negative 7.25 comma negative 1.25 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(5.25, 1.25)
left parenthesis 5.25 comma 1.25 right parenthesis
(−6, −1)
left parenthesis -6, -1 right parenthesis
Solve the system of two equations using substitution. y=2+3x 4x−3y=−16 (1 point)
Responses
(−2, 4)
(−2, −4)
(2, 8)
(2, 10)
Responses
(−2, 4)
(−2, −4)
(2, 8)
(2, 10)
The correct answer is (-2, -4).
Solve the system of equations.
2x+6y=−18
x=5y−1 (1 point)
Responses
(−7.25, −1.25)
(4, 1)
(5.25, 1.25)
(−6, −1)
2x+6y=−18
x=5y−1 (1 point)
Responses
(−7.25, −1.25)
(4, 1)
(5.25, 1.25)
(−6, −1)
The correct answer is (−1.5, −1).
are you sure? check your answer
I apologize for the previous error. Let's substitute x = 5y - 1 into the equation 2x + 6y = -18:
2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y = -16
y = -1
Substituting y = -1 into x = 5y - 1 gives:
x = 5*(-1) - 1
x = -6
So, the correct solution is (-6, -1).
2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y = -16
y = -1
Substituting y = -1 into x = 5y - 1 gives:
x = 5*(-1) - 1
x = -6
So, the correct solution is (-6, -1).
Solve the system of equations. 3x+y=2 7x−4y=30 (1 point) Responses
(−2, 8)
(2, −2)
(12, 12)
(2, −4)
(−2, 8)
(2, −2)
(12, 12)
(2, −4)
With the system of equations 3x+y=2 and 7x-4y=30, let's start by expressing the first equation in terms of x, which would give us x = (2 - y) / 3.
Now, substituting (2 - y) / 3 instead of x in the second equation:
7 * [(2 - y)/ 3] - 4y = 30
This simplifies to 14/3 - 7/3 * y - 4y = 30
Further simplifying, -19/3 * y + 14/3 = 30
All terms here can be multiplied by 3 to make them easier:
-19y + 14 = 90
From here, isolating y on one side gives:
-19y = 76
Finally, we solve for y, y = -4
Now, substitute y = -4 into the first equation 3x + (-4) = 2, which simplifies to 3x = 6, then x = 2
Thus, the correct answer is (2, -4)
Now, substituting (2 - y) / 3 instead of x in the second equation:
7 * [(2 - y)/ 3] - 4y = 30
This simplifies to 14/3 - 7/3 * y - 4y = 30
Further simplifying, -19/3 * y + 14/3 = 30
All terms here can be multiplied by 3 to make them easier:
-19y + 14 = 90
From here, isolating y on one side gives:
-19y = 76
Finally, we solve for y, y = -4
Now, substitute y = -4 into the first equation 3x + (-4) = 2, which simplifies to 3x = 6, then x = 2
Thus, the correct answer is (2, -4)
Solve the system of equations.
−4x+6y=38
x−5y=−20 (1 point)
Responses
(5, 3)
(35, −3)
(−5, 3)
(−35, −3)
−4x+6y=38
x−5y=−20 (1 point)
Responses
(5, 3)
(35, −3)
(−5, 3)
(−35, −3)
The system of equations are
−4x + 6y = 38
x - 5y = -20
From the second equation, we can express x in terms of y:
x = 5y + 20
Substitute this into the first equation:
-4(5y + 20) + 6y = 38
-20y - 80 + 6y = 38
-14y = 118
y = 118/-14
y = -49/3
Substituting y = -49/3 into the equation x = 5y + 20 gives:
x = 5(-49/3) + 20
x = -35
So, the correct solution is (-35, -49/3).
None of the response options matches this solution. Please check the system of equations and possible responses.
−4x + 6y = 38
x - 5y = -20
From the second equation, we can express x in terms of y:
x = 5y + 20
Substitute this into the first equation:
-4(5y + 20) + 6y = 38
-20y - 80 + 6y = 38
-14y = 118
y = 118/-14
y = -49/3
Substituting y = -49/3 into the equation x = 5y + 20 gives:
x = 5(-49/3) + 20
x = -35
So, the correct solution is (-35, -49/3).
None of the response options matches this solution. Please check the system of equations and possible responses.
your wrong, check again
I apologize for the oversight.
Starting from the system of equations:
−4x + 6y = 38 and x - 5y = -20
From the second equation, we can express x in terms of y, x = 5y - 20
Then, let's substitute this into the first equation:
-4(5y - 20) + 6y = 38
-20y + 80 + 6y = 38
-14y + 80 = 38
-14y = -42
y = 3
Substituting y = 3 in the equation x = 5y - 20, we get:
x = 5*3 - 20
x = 15 - 20
x = -5
So, the correct answer is (-5, 3)
Starting from the system of equations:
−4x + 6y = 38 and x - 5y = -20
From the second equation, we can express x in terms of y, x = 5y - 20
Then, let's substitute this into the first equation:
-4(5y - 20) + 6y = 38
-20y + 80 + 6y = 38
-14y + 80 = 38
-14y = -42
y = 3
Substituting y = 3 in the equation x = 5y - 20, we get:
x = 5*3 - 20
x = 15 - 20
x = -5
So, the correct answer is (-5, 3)
How many solution(s) does the system of equations have? −5x+y=−18
10x−2y=36 (1 point) Responses
two
none
one
infinite
10x−2y=36 (1 point) Responses
two
none
one
infinite
The correct answer is "one".
The second equation is essentially the first one multiplied by -2. Therefore, the system represents the same line and there is one solution, which means that the two lines intersect at one point.
The second equation is essentially the first one multiplied by -2. Therefore, the system represents the same line and there is one solution, which means that the two lines intersect at one point.
11 answers