## Solve each given system of equations via elimination. Write the solution. Please convert any fractions to decimals. Round any decimals to th

Question

Solve each given system of equations via elimination. Write the solution. Please convert any fractions to decimals. Round any decimals to the tenths place.

1.) y = 2x – 3 and x + y = 18

Solution: ( , )

2.) y = 0.25x and x + 4y = 8

Solution: ( , )

3.) y = x + 12 and 4x + 2y = 27

Solution: ( , )

4.) 10x + 3y = 19 and y = 2x + 5

Solution: ( , )

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2021-11-21T11:06:48+00:00
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## Answers ( )

## 1) Solution is (x, y) = (7, 11)

## 2) Solution is (x, y) = (4, 1)

## 3) Solution is (x, y) = (0.5, 12.5)

## 4) Solution is (0.25, 5.5)

Solution:1)

y = 2x – 3 ——- eqn 1

x + y = 18 ——– eqn 2

Rearrange eqn 1

2x – y = 3 ——- eqn 3

Add eqn 2 and eqn 3

x + y = 18

2x – y = 3

( + ) ————

3x = 21

x = 7

Substitute x = 7 in eqn 1

y = 2(7) – 3

y = 14 – 3

y = 11

Thus solution is (x, y) = (7, 11)

2)

y = 0.25x —— eqn 1

x + 4y = 8 ———- eqn 2

Rearrange eqn 1,

0.25x – y = 0 ——- eqn 3

Multiply eqn 3 by 4

x – 4y = 0 —- eqn 4

Add eqn 2 and eqn 4

x + 4y = 8

x – 4y = 0

( + ) ————-

2x = 8

x = 4

Substitute x = 4 in eqn 1

y = 0.25(4)

y = 1

Thus solution is (x, y) = (4, 1)

3.)

y = x + 12 ——- eqn 1

4x + 2y = 27 ——— eqn 2

Rearrange eqn 1,

x – y = -12

Multiply above by 2

2x – 2y = -24 ——- eqn 3

Add eqn 2 and eqn 3

4x + 2y = 27

2x – 2y = -24

( + ) —————

6x = 3

x = 0.5

Substitute x = 0.5 in eqn 1

y = 0.5 + 12

y = 12.5

Thus solution is (x, y) = (0.5, 12.5)

4.)

10x + 3y = 19 ——– eqn 1

y = 2x + 5 ——— eqn 2

Rearrange eqn 2

2x – y = -5

Multiply above equation by 3

6x – 3y = -15 ——- eqn 3

Add eqn 1 and eqn 3

10x + 3y = 19

6x – 3y = -15

( + ) —————-

16x = 4

x = 0.25

Substitute x = 0.25 in eqn 2

y = 2(0.25) + 5

y = 5.5

Thus solution is (0.25, 5.5)