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: ( , )

Answer 1

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)