Question

I need help on these three pages please asap. Thank you!

Answer 1

Explanation:

Example 1:

Given pair: (3;2)

{2x + 3y = 12,

{x - 4y = -5;

Make x the subject from the 2nd equation:

x = -5 + 4y

Replace x in the 1st equation:

2 × (-5 + 4y) + 3y = 12

-10 + 8y + 3y = 12

11 y = 12 + 10

11y = 22 / : 11

y = 2

y = 2x = -5 + 4 × 2 = -5 + 8 = 3

The answer: (3;2)

The given pair is the solution of the system of equations

.

Example 2:

Given pair: (0; -4)

{x + y = -4,

{x - 5y = 20;

x = -4 - y

(-4 - y) - 5y = 20

-4 - y - 5y = 20

-6y = 20 + 4

-6y = 24 / : (-6)

y = -4

y = -4x = -4 - (-4) = -4 + 4 = 0

The answer: (0; -4)

The given pair is the solution

.

Example 3:

Given pair: (3;3)

{x + 2y = 9,

{4x - y = 15;

x = 9 - 2y

4(9 - 2y) - y = 15

36 - 8y - y = 15

-9y = 15 - 36

-9y = -21 / : (-9)

`y = 2 (1)/(3)`

`x = 9 - 2 * 2 (1)/(3) = 9 - 2 * (7)/(3) = 9 - (14)/(3) = (13)/(3) = 4 (1)/(3)`

The given pair is not the solution

.

Example 4:

Given pair: (1; -2)

{2x - 3y = 8,

{3x + 2y = -1;

2x = 8 + 3y / : 2

x = 4 + 1,5y

3(4+1,5y) + 2y = -1

12 + 4,5y + 2y = -1

6,5y = -1 - 12

6,5y = -13 / : 6,5

y = -2

y = -2x = 4 + 1,5 × (-2) = 4 - 3 = 1

The given pair is the solution

.

Example 5:

Given pair: (1;5)

{5x - 2y = -5,

{3x - 7y = -32;

-2y = -5 - 5x / : (-2)

y = 2,5 + 2,5x

3x - 7(2,5 + 2,5x) = -32

3x - 17,5 - 17,5x = -32

-14,5x = -32 + 17,5

-14,5x = -14,5 / : (-14,5)

x = 1

x = 1y = 2,5 + 2,5 × 1 = 5

The given pair is the solution

.

Example 6:

Given pair: (-1; -3)

{3x + y = -6,

{2x = 1 + y;

y = -6 - 3x

2x = 1 + (-6 - 3x)

2x = 1 - 6 - 3x

2x + 3x = 1 - 6

5x = -5 / : 5

x = -1

x = -1y = -6 - 3 × (-1) = -6 + 3 = -3

The given pair is the solution