Question

Solve the following problem using the substitution method.

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

Answer 1

( -
`(1)/(4)`,
`(-5)/(4)` )

Explanation:

Substitute -3x - 2 for y

6x - 2y = 1

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

6x + 6x + 4 = 1 Combine like terms

12x + 4 = 1 Subtract 4 from both sides

12x + 4 - 4 = 1 - 4

12x = -3 Divide both sides both sides by 12

`(12x)/(12)` =
`(-3)/(12)`

x = -
`(1)/(4)`

Substitute -
`(1)/(4)` for x to solve for y

y = -3x - 2

y = (-3)
`(-1)/(4)` - 2

y =
`(3)/(4)` - 2

y =
`(3)/(4)` -
`(8)/(4)`

y =
`(-5)/(4)`

Answer 2

(x,y) = (-1/4, -5/4)

Explanation:

To solve the system of equations using the substitution method, we can start by solving one equation for one variable in terms of the other. Let's start by isolating y in the first equation:

y = -3x - 2

Now we can substitute this expression for y into the second equation:

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

Simplifying this, we get:

6x + 6x + 4 = 1

12x + 4 = 1

12x = -3

x = -3/12 = -1/4

Now we can substitute this value of x back into the first equation to solve for y:

y = -3(-1/4) - 2 = 3/4 - 2 = -5/4

So the solution of this system of equations is (x,y) = (-1/4, -5/4)

You can check this solution by substitute these values back into the original equation and check that both are correct.

Tell me if this helped :)