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5 votes
Hi! Please help me solve these with the elimination method, i’d be eternally grateful.

4x + y = 10 and 4x + 4y = 16

3x + 2y = 8 and 3x - y = 5

-2x + 3y = 8 and -4x -3y = -2

User Propstm
by
5.4k points

2 Answers

6 votes

Answer:

1) x = 2 y = 2

2) x = 2, y = 1

3) x = - 1, y = 2

Explanation:

Q 1
4x + y = 10 (1)
4x + 4y = 16 (2)

Subtract (1) from (2):

4x + 4y = 16
-
4x + y = 10
0 + 3y = 6

3y = 6 ==> y = 6/3 = 2

Substitute in Equation (2)

4x + y = 10

==> 4x + 2 = 10
==> 4x = 10 - 2

==> 4x = 8

x = 8/4 = 2

Ans: x = 2 y = 2

-------------------------------------------------------------------------------------------------

Q2
3x + 2y = 8 (1)
3x - y = 5 (2)

Subtract (2) from (1)
3x + 2y -(3x -y) = 8 - 5

3x + 2y - 3x -(-y) =3

3x - 3y + 2y + y = 3

3y = 3 ==> y = 1

Substitute for y in (2)
3x - y = 5
=> 3x - 1 = 5

=> 3x = 5 + 1

=> 3x = 6

=> x = 6/3 = 2

Ans: x = 2, y = 1

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Q3

-2x + 3y = 8 (1)
-4x - 3y = -2 (2)

Add (1) and (2)
-2x + 3y + (-4x -3y) = 8 + (-2)

-2x + 3y - 4x - 3y = 6

-2x - 4x + 3y - 3y = 6
-6x = -6

x = 6/-6 = -1

Substitute in (1)

-2(-1) + 3y = 8

=> 2 + 3y = 8

=> 3y = 8-2

=> 3y = 6

y = 6/3 = 2

Ans: x = -1, y = 2

User Daniel Watrous
by
4.8k points
0 votes

Answer:

(2, 2 ) , (2, 1 ) , (- 1, 2 )

Explanation:

4x + y = 10 → (1)

4x + 4y = 16 → (2)

multiplying (1) by - 1 and adding to (2) will eliminate x

- 4x - y = - 10 → (3)

add (2) and (3) term by term to eliminate x

0 + 3y = 6

3y = 6 ( divide both sides by 3 )

y = 2

substitute y = 2 into either of the 2 equations and solve for x

substituting into (1)

4x + 2 = 10 ( subtract 2 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

solution is (2, 2 )

----------------------------------------------------------------------

3x + 2y = 8 → (1)

3x - y = 5 → (2)

multiplying (2) by 2 and adding to (1) will eliminate y

6x - 2y = 10 → (3)

add (1) and (3) term by term to eliminate y

9x + 0 = 18

9x = 18 ( divide both sides by 9 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (1)

3(2) + 2y = 8

6 + 2y = 8 ( subtract 6 from both sides )

2y = 2 ( divide both sides by 2 )

y = 1

solution is (2, 1 )

----------------------------------------------------------------------------

- 2x + 3y = 8 → (1)

- 4x - 3y = - 2 → (2)

adding (1) and (2) term by term will eliminate y

- 6x + 0 = 6

- 6x = 6 ( divide both sides by - 6 )

x = - 1

substitute x = - 1 into either of the 2 equations and solve for y

substituting into (1)

- 2(- 1) + 3y = 8

2 + 3y = 8 ( subtract 2 from both sides )

3y = 6 ( divide both sides by 3 )

y = 2

solution is (- 1, 2 )

User Gcali
by
5.2k points
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