Question

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.

Answer 1

Answer:

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 answer: 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 answer: 1=x, or x=1.