Question

How do you solve `-3w+ z=4` and `-9w+ 5z= -1`?

Answer 1

See a solution process below:

Explanation:

Step 1)Solve both equations for `-9w`:

• Equation 1:

`-3w + z = 4`

`color(red)(3)(-3w + z) = color(red)(3) xx 4`

`(color(red)(3) xx -3w) + (color(red)(3) xx z) = 12`

`-9w + 3z = 12`

`-9w + 3z - color(red)(3z) = 12 - color(red)(3z)`

`-9w + 0 = 12 - 3z`

`-9w = 12 - 3z`

• Equation 2:

`-9w + 5z = -1`

`-9w + 5z - color(red)(5z) = -1 - color(red)(5z)`

`-9w + 0 = -1 - 5z`

`-9w = -1 - 5z`

Step 2)* Now that the left side of each equation is equal we can equate the right side of each equation and solve for `z`

`12 - 3z = -1 - 5z`

`12 - color(red)(12) - 3z + color(blue)(5z) = -1 - color(red)(12) - 5z + color(blue)(5z)`

`0 + (-3 + color(blue)(5))z = -13 - 0`

`2z = -13`

`(2z)/color(red)(2) = -13/color(red)(2)`

`(color(red)(cancel(color(black)(2)))z)/cancel(color(red)(2)) = -13/2`

`z = -13/2`

Step 3) Substitute `-13/2` for `z` in the solution to either equation in Step 1 and solve for `w`:

`-9w = 12 - 3z` becomes:

`-9w = 12 - (3 xx -13/2)`

`-9w = 12 - (-39/2)`

`-9w = 12 + 39/2`

`-9w = (2/2 xx 12) + 39/2`

`-9w = 24/2 + 39/2`

`-9w = (24 + 39)/2`

`-9w = 63/2`

`1/color(red)(-9) xx -9w = 1/color(red)(-9) xx 63/2`

`1/cancel(color(red)(-9)) xx color(red)(cancel(color(black)(-9)))w = -63/18`

`w = -7/2`

The Solution Is:

`w = -7/2` and `z = -13/2`