Question

3x+6y=5
-3x-3y=7

Solve the systems of equations

Answer 1

x = -19/3, y = 4

Explanation:

Answer 2

`x = -(19)/(3), y = 4` or
`(-(19)/(3), 4)`

Explanation:

Given the systems of linear equations, 3x + 6y = 5 and -3x - 3y = 7:

Equation 1: 3x + 6y = 5

Equation 2: -3x - 3y = 7

The best method to use for the given system is the process of elimination, since the coefficients of x in both equations have opposite signs.

Step 1: Add both equations:

3x + 6y = 5

-3x - 3y = 7

3y = 12

Step 2: Divide both sides by 3:

`(3y)/(3) = (12)/(3)`

y = 4

Step 3: Substitute the value of y into Equation 1:

3x + 6y = 5

3x + 6(4) = 5

3x + 24 = 5

Step 4: Subtract 24 from both sides:

3x + 24 - 24 = 5 - 24

3x = -19

Step 5: Divide both sides by 3:

`(3x)/(3) = (-19)/(3)`

`x = -(19)/(3)`

Verify the validity of x and y as solutions:

Verify whether the values for x and y satisfy both equations:
`x = -(19)/(3), y = 4`

Equation 1: 3x + 6y = 5

`3(-(19)/(3)) + 6(4) = 5`

-19 + 24 = 5

5 = 5 (True statement).

Equation 2: -3x - 3y = 7

`-3(-(19)/(3)) - 3(4) = 7`

19 - 12 = 7

7 = 7 (True statement).

Therefore, the solutions to the given systems of linear equations are:
`x = -(19)/(3), y = 4`, or
`(-(19)/(3), 4)`.