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

To solve the system using substitution method, you need to solve one equation for x and substitute it into the other equation. Therefore, the correct answer is option d) 2(4y - 9) + 5y = 6.

Step-by-step explanation:

To solve the system of equations using substitution method, we first solve one of the equations for x and substitute it into the other equation:

1. From the first equation, solve for x: x = 9 - 4y
2. Substitute this expression for x in the second equation:
   2(9 - 4y) + 5y = 6
3. Simplify the equation:
   18 - 8y + 5y = 6
4. Combine like terms:
   -3y + 18 = 6
5. Isolate y by subtracting 18 from both sides:
   -3y = -12
6. Divide both sides by -3 to solve for y:
   y = 4
7. Substitute the value of y back into x = 9 - 4y:
   x = 9 - 4(4) = -7

Therefore, the correct answer is option d) 2(4y - 9) + 5y = 6.