Solve the system of two equations using substitution.
y=2+3x
4x−3y=−16 (1 point)
Responses
(2, 8)
left parenthesis 2 comma 8 right parenthesis
(−2, 4)
left parenthesis negative 2 comma 4 right parenthesis
(2, 10)
left parenthesis 2 comma 10 right parenthesis
(−2, −4)
To solve the system of equations using substitution, we first solve one equation for one variable and substitute it into the other equation.
Given the equation y = 2 + 3x, we can solve this equation for y by subtracting 3x from both sides:
y - 3x = 2
So, y = 2 + 3x.
Next, substitute this expression for y into the second equation 4x - 3y = -16:
4x - 3(2 + 3x) = -16
4x - 6 - 9x = -16
-5x - 6 = -16
-5x = -10
x = -10 / -5
x = 2
Now that we have the value of x, we can substitute it back into the equation y = 2 + 3x to find the value of y:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is (2, 8).
Solve the system of equations.
2x+6y=−18
x=5y−1 (1 point)
Responses
(−6, −1)
left parenthesis negative 6 comma negative 1 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(5.25, 1.25)
left parenthesis 5.25 comma 1.25 right parenthesis
(−7.25, −1.25)
To solve the system of equations, we can substitute the value of x from the second equation into the first equation.
Given the equation x = 5y - 1, we can substitute this expression for x in the first equation 2x + 6y = -18:
2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -16 / 16
y = -1
Now that we have the value of y, we can substitute it back into the second equation x = 5y - 1 to find the value of x:
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution to the system of equations is (-6, -1).
Solve the system of equations.
3x+y=2
7x−4y=30 (1 point)
Responses
(2, −4)
left parenthesis 2 comma negative 4 right parenthesis
(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis
(2, −2)
left parenthesis 2 comma negative 2 right parenthesis
(12, 12)
To solve the system of equations, we can use the method of substitution.
Given the first equation 3x + y = 2, we can solve this equation for y in terms of x:
y = 2 - 3x (equation 1)
Now, substitute this expression for y into the second equation 7x - 4y = 30:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 38 / 19
x = 2
Now that we have the value of x, we can substitute it back into equation 1 to find the value of y:
y = 2 - 3(2)
y = 2 - 6
y = -4
Therefore, the solution to the system of equations is (2, -4).
Solve the system of equations.
−4x+6y=38
x−5y=−20 (1 point)
Responses
(35, −3)
left parenthesis 35 comma negative 3 right parenthesis
(−35, −3)
left parenthesis negative 35 comma negative 3 right parenthesis
(5, 3)
left parenthesis 5 comma 3 right parenthesis
(−5, 3)
Are you sure?
I apologize for the mistake in my previous response. Let's solve the system of equations correctly.
Given the equations:
-4x + 6y = 38 (equation 1)
x - 5y = -20 (equation 2)
From equation 2, we can solve for x:
x = -20 + 5y (equation 3)
Now substitute this expression for x into equation 1:
-4(-20 + 5y) + 6y = 38
80 - 20y + 6y = 38
-20y + 6y = 38 - 80
-14y = -42
y = -42 / -14
y = 3
Next, substitute this value of y into equation 3 to find x:
x = -20 + 5(3)
x = -20 + 15
x = -5
Therefore, the correct solution to the system of equations is (-5, 3).
How many solution(s) does the system of equations have?
−5x+y=−18
10x−2y=36 (1 point)
Responses
one
one
infinite
infinite
none
none
two