Question

What is the value of q in the solution to this system of equations?

2m - 5q = 8
4m + 2q = 64

Answer 1

q = 4

Explanation:

Step 1: Set up the equation

• The system of equations can be solved algebraically by substitution or elimination.
• For substitution, solve one of the equations for m and plug it into the other equation in order to solve for q.
• For elimination, cancel the m terms in order to solve for q.

Step 2: Solve for q

• Substitution:

• 2m - 5q = 8
• 4m + 2q = 64

1. 4m = 64 - 2q
2. m =
   `(64-2q)/(2)`
3. m = 16 -
   `(1)/(2)`q
4. 2(16 -
   `(1)/(2)`q) - 5q = 8
5. 32 - q - 5q = 8
6. -6q = -24
7. q = 4

• Elimination:
• 2m - 5q = 8 (multiply whole equation by -2 in order cancel m terms)
• 4m + 2q = 64
• -2(2m - 5q = 8)

1. -4m + 10q = -16
2. 4m + 2q = 64
3. 12q = 48
4. q = 4

Answer 2

16 because you do 4*16=64
q=3 because