Carlos decided to solve the following system using substitution.
2x + 3y = 12
x = 2y – 9
Which equation is a correct following step to solve the system?
A. 2·2y – 9 + 3y = 12
Incorrect. You did not put parentheses around the entire expression 2y – 9.
B. 4y – 9 + 3y = 12
Incorrect. You did not distribute the coefficient 2 to both 2y and -9.
C. 4xy – 18x + 3y = 12
Incorrect. You forgot to remove the variable x when you substituted the expression 2y – 9.
Which equation is a correct step to solve the following system using substitution?
y = x2 + 4
y = 6x – 1
A
Incorrect. The purpose of substitution is to replace one of the variables. You added the two equations and you still have both variables.
B
Incorrect. The purpose of substitution is to replace one of the variables. You attempted to subtract the two equations but made an error in the process.
C
Correct! You correctly replaced the y in the second equation with its equivalent expression from the first equation.
D
Incorrect. You replaced x with an expression equivalent to y.
Solve the following system of equations using substitution.
y = 2x2 + 4x – 7
y = 5 – x
A. (-4, 9) & (3, 2)
Incorrect. When the leading coefficient is a value other than 1, at least one of the solutions will be fractional.
B. (-4, 9) & (1.5, 3.5)
Correct! These are the two points where these two equations are equal in value.
C. (4, 1) & (1.5, 3.5)
Incorrect. You made sign errors when solving the system.
D. (-1.5, 6.5) & (4, 1)
Incorrect. You did not set your factors equal to zero and solve for x.
Solve the following system of equations using substitution..
2x – 3y = 6
y = x – 5
A. (9, 4)
Correct! This point is the intersection of the two lines and satisfies both equations.
B. (-11, -16)
Incorrect. -3 was not distributed to both terms in the quantity (x – 5).
C. (-22, -27)
Incorrect. You made sign errors when solving the system.
D. (1, -4)
Incorrect. -3 was not distributed to both terms in the quantity (x – 5).