Answer:
Solve for x in the first equation. ⇒ the first answer
Step-by-step explanation:
* Lets study how to solve the system of the equation using
the substitution method
- The first equation is ax + by = c
- The second equation is dx + ey = f
* To chose the first step
- Solve for x or y depends on the integer answer
EX: ax = c - by ⇒ x = c/a - (b/a)y
b/a = integer , c/a = integer ⇒ best choice
- If not solve for next variable
EX: by = c - ax ⇒ y = c/b - (a/b)y
a/b = integer , c/b = integer ⇒ best choice
- If not repeat with the second equation to find the best choice
* Lets check our equations:
∵ -9x + 4y = 10 ⇒ (1)
∵ -9x + 3y = 3 ⇒ (2)
* If we start with the first equation and solve for x
∵ -9x = 10 - 4y ⇒ (2)
- It will be difficult if we divide by -9, but the second equation
has -9x, so we will solve of -9x not for x and substitute the value
of -9x in the second equation
* Substitute (3) in (2)
∴ 10 - 4y + 3y = 3 ⇒ collect the like terms
∴ -y = -7 ⇒ y = 7
substitute the value of in (3)
∴ -9x = 10 - 4(7) ⇒ -9x = -18 ⇒ ÷ -9 in both sides
∴ x = 3
∴ The best choice to avoid fraction is:
Solve for x in the first equation.
, where I is the identity matrix (1s on the diagonal, 0s elsewhere)