Solving Systems of Equations by Substitution

Question

Hello, I'm having trouble figuring out how to solve this word problem. If you could explain in-depth step by step that would be helpful. Thanks in advance! The system of equation is: 8t + 5h = 220 and 5t +h = 112.

Skyler buys 8 T-Shirts and 5 hats for $220. The next day, he buys 5 T-shirts and 1 hat for $112. Use the system of equations to find the cost of each T-shirt and each hat.

Answer 1

8t + 5h = 220

5t + h = 112

By substitution:

h = 112 - 5t

8t + 5h = 220

8t + 5(112 - 5t) = 220

8t + 560 - 25t = 220

-17t + 560 =220

-17t = =340

t = 20

then h = 112 - 5t = 112 - 5(20)

= 112 - 100

= 12

hat costs $12; t-shirt costs $20

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By Elimination:

Multiplies second equation by -5:

8t + 5h = 220

-5( 5t + h = 112)

Result is:

8t + 5h = 220

-25t + -5h = -560

Adding them together:

-17t = -340

Then t = 20

Per original 1st equation:

8(20) + 5h = 220

160 + 5h = 220

5h = 60

h = 12

(same answers)

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CHECK

8*20 + 5*12 = 160 + 60 = 220

5*20 + 12 = 100+12 = 112

so yes the answers checks