What is the best first step for solving the given system using substitution while avoiding fractions - 9x+4y=10 - 9x+3y=3

Solve for x in the first equation.

Solve for y in the first equation.

Solve for x in the second equation.

Solve for y in the second equation.

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.

B is the answer