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, −4)
left parenthesis negative 2 comma negative 4 right parenthesis
(2, 10)
To solve the system of equations using substitution, we will first solve one of the equations for one variable and then substitute that expression into the other equation.
From the first equation, y = 2 + 3x, we can solve for y by subtracting 2 and dividing by 3, yielding:
y = 2 + 3x
y - 2 = 3x
x = (y - 2)/3
Now we substitute this expression for x in the second equation:
4x - 3y = -16
4((y - 2)/3) - 3y = -16
(4/3)(y - 2) - 3y = -16
(4/3)y - 8/3 - 3y = -16
(4/3)y - 9y/3 = -16
[(4 - 9)y]/3 = -16
(-5y)/3 = -16
-5y = -48
y = 48/5
y = 9.6
Now we substitute this value of y back into the expression we found for x:
x = (y - 2)/3
x = (9.6 - 2)/3
x = 7.6/3
x = 2.533...
So the solution to the system of equations is approximately (2.533, 9.6). Therefore, the correct response is:
(2.533, 9.6)
are you sure
Apologies for the confusion in my previous response. Let's solve the system of equations using substitution again:
Given:
y = 2 + 3x
4x - 3y = -16
We can solve the first equation for x:
y = 2 + 3x
3x = y - 2
x = (y - 2)/3
Now we substitute this expression for x in the second equation:
4x - 3y = -16
4((y - 2)/3) - 3y = -16
(4/3)(y - 2) - 3y = -16
(4/3)y - 8/3 - 3y = -16
(4/3)y - 9y/3 = -16
[(4 - 9)y]/3 = -16
(-5y)/3 = -16
-5y = -48
y = 48/5
y = 9.6
Now we substitute this value of y back into the expression we found for x:
x = (y - 2)/3
x = (9.6 - 2)/3
x = 7.6/3
x = 2.533...
So the correct solution to the system of equations is approximately (2.533, 9.6). Therefore, the correct response is:
(2.533, 9.6)
They are choices stupid
Apologies for the misunderstanding. Let's substitute the expression for y in terms of x into the second equation and solve for x:
Given:
y = 2 + 3x
4x - 3y = -16
Substitute y = 2 + 3x into the second equation:
4x - 3(2 + 3x) = -16
4x - 6 - 9x = -16
-5x - 6 = -16
-5x = -10
x = 2
Now substitute x = 2 back into the first equation to solve for y:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is (2, 8). The correct response is:
(2, 8)