Solve the system of two equations using substitution.
y=2+3x
4x−3y=−16(1 point)
Responses
(2, 10)
left parenthesis 2 comma 10 right parenthesis
(−2, −4)
left parenthesis negative 2 comma negative 4 right parenthesis
(2, 8)
left parenthesis 2 comma 8 right parenthesis
(−2, 4)
(2, 8)
Solve the system of equations.
2x+6y=−18
x=5y−1 (1 point)
Substitute x=5y-1 into the first equation:
2(5y-1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1
Now substitute y = -1 into x = 5y - 1:
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution is x = -6, y = -1.
Solve the system of equations.
3x+y=2
7x−4y=30(1 point)
Responses
(2, −2)
left parenthesis 2 comma negative 2 right parenthesis
(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis
(2, −4)
left parenthesis 2 comma negative 4 right parenthesis
(12, 12)
Let's use the substitution method.
From the first equation:
3x + y = 2
y = 2 - 3x
Substitute y = 2 - 3x into the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 38 / 19
x = 2
Now, substitute x = 2 back into y = 2 - 3x:
y = 2 - 3(2)
y = 2 - 6
y = -4
Therefore, the solution to the system of equations is x = 2 and y = -4.
The correct response is (2, -4).
Solve the system of equations.
−4x+6y=38
x−5y=−20(1 point)
Responses
(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis
(5, 3)
left parenthesis 5 comma 3 right parenthesis
(35, −3)
left parenthesis 35 comma negative 3 right parenthesis
(−35, −3)
Let's solve this system of equations using the substitution method.
From the second equation:
x - 5y = -20
x = 5y - 20
Substitute x = 5y - 20 into the first equation:
-4(5y - 20) + 6y = 38
-20y + 80 + 6y = 38
-14y + 80 = 38
-14y = -42
y = -42 / -14
y = 3
Now substitute y = 3 into x = 5y - 20:
x = 5(3) - 20
x = 15 - 20
x = -5
Therefore, the solution to the system of equations is x = -5 and y = 3.
The correct response is (-5, 3).
How many solution(s) does the system of equations have?
−5x+y=−18
10x−2y=36(1 point)
Responses
none
none
one
one
infinite
infinite
two
To determine the number of solutions, let's check if the two equations represent parallel lines. We'll compare the slopes of the two equations.
The first equation: -5x + y = -18
Rearranging to y = 5x - 18, the slope is 5.
The second equation: 10x - 2y = 36
Rearranging to y = 5x - 18, the slope is 5 as well.
Since the slopes of the two equations are the same, the lines are parallel, and they will not intersect. This means there are no solutions to the system of equations.
The correct response is "none."