Question

Please help me find the answer pls​

Answer 1

A. Solutions are: x = 2, y = 1.

B. Solutions are: x = 3, y = 2.

C.

1. Inconsistent

2. Inconsistent

3. Consistent

Explanation:

A. Solutions of each system of linear equations by substitution method:

Equation 1: 3x - 2y = 4

Equation 2: x = 2y

Step 1: Substitute x = 2y into the Equation 1:

3(2y) - 2y = 4

6y - 2y = 4

4y = 4

Step 2: Divide both sides of the equation by 4 to isolate y:

`(4y)/(4) = (4)/(4)`

y = 1.

Step 3: For Equation 2, x = 2y, substitute y = 1 into the equation to solve for x:

x = 2y

x = 2(1)

x = 2

Therefore, the solutions are: x = 2, y = 1.

B. Find the solutions of each system of linear equations by elimination method:

Equation 1: 2x + y = 8

Equation 2: x + y = 5

Step 1: Multiply Equation 2 by 2:

2(x + y) = 5(2)

2x + 2y = 10

Step 2: Subtract Equation 1 from the equation derived from Step 1, 2x + 2y = 10:

2x + 2y = 10

- 2x + y = 8

y = 2

Step 3: Plug in y = 2 into Equation 1, 2x + y = 8 to solve for x:

2x + y = 8

2x + (2) = 8

Step 4: subtract both sides of the equation by 2 to isolate x:

2x + 2 - 2 = 8 - 2

2x = 6

Step 5: Divide both sides of the equation by 2 to solve for x:

`(2x)/(2) = (6)/(2)`

x = 3.

The solutions are: x = 3, y = 2.

C:

1. Inconsistent

2. Inconsistent

3. Consistent (infinitely many solutions)