Question

Show all your work plz!! Use the Substitution method to solve the system of equations. x + y = 20 30x + 25y = 550

Answer 1

solution is (x, y ) = (10, 10)

given

x + y = 20 → (1)

30x + 25y = 550 → (2)

from (1) y = 20 - x → (3)

substitute y = 20 - x in (2)

30x + 25(20 - x) = 550

30x + 500 - 25x = 550

5x + 500 = 550 ( subtract 500 from both sides )

5x = 50 ( divide both sides by 5 )

x =
`(50)/(5)` = 10

substitute x = 10 in (3) : y = 20 - 10 = 10

thus x = 10, y = 10 is the solution

Answer 2

x + y = 20

30x + 25y = 550

Using the first equation, we can find a temporary value of x.

x = 20 - y

Now that we have a value of x, we can plug it into the second equation to find the exact value of y.

30x + 25y = 550

30(20 - y) + 25y = 550

Distributive property.

600 - 30y + 25y = 550

Combine like terms.

600 - 5y = 550

Add 5y to both sides.

600 = 550 + 5y

Subtract 550 from both sides.

50 = 5y

Divide both sides by 5.

y = 10.

Now we can plug the value of y into the original equation to find the value of x.

10 + x = 20

Subtract 10 from both sides.

x = 10

The value of x is equal to 10, and the value of y is also equal to 10.