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3 years ago

System of equations ( substitution methods) can someone solve these problems x=3y-5 ; x+y=3 y=x ; 3x+3y=18 y=3x+4 ; 5x-y=0

Mathematics

1 answer:

azamat3 years ago

5 0

Answer:

(1,2)

(3,3)

(-1/2, 11/2)

Step-by-step explanation:

A system of equations is 2 or more equations for which the same x,y solution exists. We can solve the system in three ways: elimination, substitution, or graphing. Substitution can be used by substituting the value of one variable into the equation.

Pair x=3y-5 and x+y=3

Because x=3y-5, we can substitute 3y-5 into x in x+y=3

x+y=3

(3y-5)+y=3

3y-5+y=3

4y-5=3

4y-5+5=3+5

4y=8

y=2

We now substitute y=2 into x=3y-5.

x=3y-5

x=3(2)-5

x=6-5

x=1

Pair y=x and 3x+3y=18

Because y=x, we can substitute x into y in 3x+3y=18

3x+3y=18

3x+3x=18

6x=18

x=3

We now substitute x=3 into y=x.

y=3.

Pair y=-3x+4 and 5x-y=0

Because y=-3x+4, we can substitute -3x+4 into y in 5x-y=0

5x-y=0

5x-(-3x+4)=0

5x+3x+4=0

8x+4=0

8x=-4

x=-1/2

We now substitute x=-1/2 into y=-3x+4

y=-3x+4

y=-3(-1/2)+4

y=3/2+4

y=11/2

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Chase goes out to lunch. The bill, before tax and tip, was $11.90. A sales tax of 9% was added on. Chase tipped 17% on the amoun

WINSTONCH [101]

Answer:

$15.17

Step-by-step explanation:

First we calculate the value for the sales tax:

$11.90 \times \frac{9}{100 } = 1.07$

we then add the value for the sales tax ($1.07) to the initial bill:

$11.90 + 1.07 = 12.97$

We were instructed to calculate the tip after the sales tax was added so:

$12.97 \times \frac{17}{100} = 2.20$

after we will add the value for the tip to the value that we have for the bill ( this is the new value that includes the sales tax) to find the total cost:

$12.97+ 2.20 = 15.17$