Question

How do you solve the following linear system: `6x-4y=-3 , x+4y=1`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve each equation for an "easy", common term, in this problem we can use `4y`

• Equation 1:

`6x - 4y = -3`

`6x + color(blue)(3) - 4y + color(red)(4y) = -3 + color(blue)(3) + color(red)(4y)`

`6x + 3 - 0 = 0 + 4y`

`6x + 3 = 4y`

`4y = 6x + 3`

• Equation 2:

`x + 4y = 1`

`x - color(red)(x) + 4y = 1 - color(red)(x)`

`0 + 4y = 1 - x`

`4y = 1 - x`

Step 2) Because the left side of both equations are the same we can equate the right sides of the two equations and solve for `x`:

`6x + 3 = 1 - x`

`6x + color(blue)(x) + 3 - color(red)(3) = 1 - color(red)(3) - x + color(blue)(x)`

`6x + color(blue)(x) + 0 = -2 - 0`

`6x + color(blue)(x) = -2`

`6x + color(blue)(1x) = -2`

`(6 + color(blue)(1))x = -2`

`7x = -2`

`(7x)/color(red)(7) = -2/color(red)(7)`

`x = -2/7`

Step 3) Substitute `-2/7` for `y` in the solution to either equation in Step 1:

`4y = 1 - x` becomes:

`4y = 1 - (-2/7)`

`4y = 1 + 2/7`

`4y = 7/7 + 2/7`

`4y = 9/7`

`color(red)(1/4) xx 4y = color(red)(1/4) xx 9/7`

`4/color(red)(4)y = 9/28`

`y = 9/28`

The Solution Is:

`x = -2/7` and `y = 9/28`

Or

`(-2/7, 9/28)`