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.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18