Question

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the first equation is substituted into the second equation.

x + 4y = 9
2x + 5y = 6


A. 2x + 5(4y 9) = 6
B. 2x + 5(4y 9) = 6
C. 2(4y 9) + 5y = 6
D. 2(4y 9) + 5y = 6

Answer 1

The substitution method involves solving one of the equations for a variable, and then substituting it into the other equation. In this case, after substituting x with 9 - 4y into the second equation, the new equation is 2(9 - 4y) + 5y = 6, which is option C.

Step-by-step explanation:

To solve the system of equations using the substitution method, we first need to solve one of the equations for a single variable. In this case, we can solve the first equation x + 4y = 9 for x which gives us x = 9 - 4y. Then, we substitute this expression for x in the second equation 2x + 5y = 6.

Substituting the expression into the second equation, we get 2(9 - 4y) + 5y = 6. Simplifying this, we have 18 - 8y + 5y = 6, which leads to -3y = -12, and finally dividing both sides by -3 gives us y = 4. We can then substitute y back into our original expression for x, giving us x = 9 - 4(4) and x = 9 - 16, which simplifies to x = -7. From the given multiple choice options, after substituting x = 9 - 4y into the second equation, the new equation should be 2(9 - 4y) + 5y = 6, which corresponds to option C.