Question

How do you solve the following linear system: #-x + 4y = -8 , 3x + 2y = 9 #?

Answer 1

Substitution.

Explanation:

Substitution Method
Solve for `x` in the equation `-x + 4y = -8`.

Subtract `4y` from both sides: `-x = -4y - 8`
Divide both sides by `-1`: `x = 4y + 8`
Now, knowing that `x = 4y + 8`, replace `x` in the other equation with `4y + 8`.

This gives: `3(4y + 8) + 2y = 9`
Distribute: `12y + 24 + 2y = 9`
Combine like terms on the left side: `14y + 24 = 9`
Subtract `24` from both sides: `14y = -15`
Divide both sides by `14`: `color(red)(y = -15/14)`

Now, plug in your new value for `y` in either equation.
Example: `3x + 2(-15/14) = 9`
Multiply: `3x + (-30/14) = 9`
Simplify: `3x - 15/7 = 9`
Add `15/7` to both sides and find a common denominator: `3x = 15/7 + 63/7`
Add: `3x = 78/7`
Divide both sides by `3`: `x = 78/15`
Simplify: `color(red)(x = 26/5)`