Which systems of equations have no solutions? (check all that apply.)

x – y = 1, –3x + 3y = 3

2y = 3 – 4x, x + y = 0

12x + 2 = 4y – 10, 2x + y = –11

–3x – y = 5, 15x = 10 – 5y

x + y = 1, –4x + 2y = 7

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 : )

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