Tyler and Han are trying to solve this system by substitution: x+3y=-5 9x+3y=3 Tyler's first step is to isolate x in the first equation to get x=-5-3y. Han's first step is to isolate 3y in the first equation to get 3y=-5-x. Show that both first steps can be used to solve the system and will yield the same solution.

Yes, they can both be solved and get the same answer.

Step-by-step explanation:

Tyler's way:

Since Tyler solved first by isolating x, resulting in x=-5-3y, he can then go and look at the second equation and solve for y there. In the second equation you're going to want to subtract 9x from the right side and left side to then get 3y=3-9x. Now you're going to divide by 3 on both sides to isolate y. You'll get y=1-3x. Now we know what y equals. Plug that back into the first equation and you'll get x=-5-3(1-3x). Use the distributive property to simplify that and you'll get x=-5-3+9x. That simplified is x=-8+9x. Add 8 on both sides and you'll get 8+x=9x. Subtract x from the both sides and you'll get 8=8x. Divide by 8 on both sides and you'll get the final 1=x, or x=1.

Han's way:

Since Han solved first by isolating 3y, resulting in 3y=-5-x, he can then go and look at the second equation and solve for y there. In the second equation you're going to want to subtract 9x from the right side and left side to then get 3y=3-9x. Now you're going to divide by 3 on both sides to isolate y. You'll get y=1-3x. Now we know what y equals. Plug that back into the first equation and you'll get 3(1-3x)=-5-x. Use the distributive property to simplify that and you'll get 3-9x=-5-x. Add 9x to both sides and you'll get 3=-5+8x. Add 5 to both sides to isolate 8x and you'll get 8=8x. Divide by 8 on both sides and you'll get the final 1=x, or x=1.

Determine if both first steps can be used to solve the system and will yield the same solution

Both Tyler and Han's first step can be used to solve the system and will yield the same solution

Given:

x + 3y = -5

x + 3y = -5 9x + 3y = 3

Tyler

isolate x in the first equation to get

x = -5 - 3y

substitute into second equation

9x + 3y = 3

9( -5 - 3y) + 3y = 3

-45 - 27y + 3y = 3

- 24y = 3 + 45

-24y = 48

y = 48/-24

y = -2

Recall,

x = -5 - 3y

= -5 - 3(-2)

= -5 + 6

x = 1

Han:

isolate 3y in the first equation to get

3y = - 5 - x

substitute into second equation

9x + 3y = 3

9x + (-5 - x) = 3

9x -5 - x = 3

8x = 3 + 5

8x = 8

x = 1

Recall,

3y = - 5 - x

3y = -5 - (1)

3y = -5 - 1

3y = - 6

y = -2

Therefore, both first steps can be used to solve the system and will yield the same solution.

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