Please help I will give out brainliest

All the points change, there are no invariant points

Step-by-step explanation:

The given parameters are

To translate the square OABC by the vector  , we have;

The coordinates of the point O is (0, 0)

The coordinates of the point A is (3, 0)

The coordinates of the point B is (3, 3)

The coordinates of the point C is (0. 3)

The translation is by moving 1 step right and three steps up to give;

O' is (0+1, 0+3) which is (1, 3)

A' is (3+1, 0+3) which is (4, 3)

B' is (3+1, 3+3) which gives (4, 6)

C' is (0+1, 3+3) which gives (1, 6)

As all the points change, there are no invariant points and the number of invariant points is zero.

These are all Called Systems of Equations in Mathematics:

Q1.). Solve: x – y = 1, –3x + 3y = 3 ===> There is No Solutions

I will try to solve your equations:

x - y = 1;

- 3x + 3y = 3

Step 1: Solve

x - y = 1 for x:

x - y + y = 1 + y (Add: Y, to both sides:)

x = y + 1

Step 2: Substitute Y + 1 for X in - 3x + 3y = 3

- 3x + 3y = 3

-3 ( y + 1) + 3y = 3

- 3 = 3 (Simplify both sides)

- 3 + 3 = 3 + 3 (Add 3 to both sides):

When Graph: y = x - 1; y = x + 1

0 = 6 ===> Therefore, Answer, No Solutions to this Equation.

Q2). Solve: 2y = 3 – 4x, x + y = 0

Solve: your system of equation:

x + y = 0; 2y = -4x + 3

Step 1: Solve: x + y = 0 for x:

x + y + - y = 0 + - y ( Add - y, to both sides)

x = - y

Step 2: Substitute: - y for x in 2y = - 4x + 3:

2y = - 4x + 3

2y = - 4 ( - y ) + 3

2y = 4y + 3 ( Simplify both sides of equation: ):

2y + - 4y = 4y + 3 + - 4y ( Add - 4y to both sides):

- 2y = 3

- 2y / 2 = 3 / - 2 ( Divide both sides by - 2 )

y = - 3 / 2

Step 3: Substitute: - 3 / 2 for y in x = - y

x = - y

x = - -3 / 2

x = 3/2 (Simplify both sides)

When Graph: y = - 2x + 1.5; y = -x

> x = 3 / 2; and y = -3 / 2

Q 3:). Solve: 12x + 2 = 4y – 10; 2x + y = –11

Solve equation:

2x + y = - 1; 12x + 2 = 4y - 10

Step 1: Solve: 2x + y = - 1 for y:

2x + y + -2x = - 1 + - 2x ( Add -2x to both sides ):

y = -2x - 1

Step 2: Substitute: - 2x - 1 for y in 12x + 2 = 4y - 10:

12x + 2 = 4y - 10

12x + 2 = 4 ( - 2x - 1 ) - 10

12x + 2 = -8x - 14 ( Simplify Both Sides:):

12x + 2 + 8x = -8x - 14 + 8x ( Add 8x to both sides:):

20x + 2 = -14

20x + 2 -2 = -14 + -2 ( Add -2 to both sides:):

2ox = -16

20x / 20 = -16 / 20 (Divide both sides by 20:):

x = -4 / 5

Step 3: Substitute: - 4 / 5 for X in y = - 2x - 1:

y = -2x - 1

y = -2 ( -4 / 5 ) - 1

y = 3 / 5 ( Simplify both sides):

When Graph: y = 3x + 3; y = -2x - 1

Therefore, Answer, y = 3 / 5 and x = -4 / 5

Q4.). Solve: –3x – y = 5; 15x = 10 – 5y > There is No Solutions:

Solve your equation:

-3y - y = 5; 15x = -5y + 10

Step 1: Solve: -3x - y = 5 for y:

-3x - y + 3x = 5 + 3x ( Add 3x to both sides:):

-y = 3x + 5

-y / -1 = 3x + 5 / -1 (Divide both sides by -1):

y = -3x - 5

Step 3: Substitute: -3x - 5 for y in 15x = -5y + 10:

15x = -5y + 10

15x = -5 ( -3x - 5) + 10

15x = 15x + 35 ( Simplify both sides):

15x + -15x = 15x + 35 + -15x ( Add -15x Both sides):

0 = 35

When Graph: y = -3x - 5; y = -3x + 2

Therefore, Answer, No Solutions to this Equation:

Q 5.). Solve: x + y = 1; –4x + 2y = 7

Solve your Equation:

x + y = 1; -4x + 2y = 7

Step 1: Solve: x + y + -y = 1 + -y ( Add -y both sides ):

x = -y + 1

Step 2: Substitute: -y + 1 for X in -4x + 2y = 7

-4x + 2y = 7

-4 ( - y + 1 ) + 2y = 7

6y - 4 = 7 (Simplify both sides):

6y - 4 + 4 = 7 + 4 ( Add 4 to both sides):

6y = 11

6y / 6 = 11 / 6 ( Divide both sides by 6 ):

y = 11 / 6

Step 4: Substitute: 11 / 6 for y in X = -y + 1

x = -y + 1

x = - 11 / 6 + 1

x = -5 / 6 (Simplify both sides ):

When Graph: y = -x + 1; y = 2x + 3

Therefore, Answer, x = -5 / 6 and y = 11 / 6

Hence, Answers to your Questions: (Q1: x – y = 1, –3x + 3y = 3 There is No Solutions) , and (Q4: –3x – y = 5, 15x = 10 – 5y, There is No Solutions.). Both, Q1; and Q4, has No Solutions to the Systems of Equations:

Hope that Helps : )