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)
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)
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)
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)
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).
Solve the system of equations. 3x+y=2 7x−4y=30 (1 point) Responses
(−2, 8)
(2, −2)
(12, 12)
(2, −4)
are you sure? check your answer
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)
Solve the system of equations.
−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.