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

1 Answer
Jun 20, 2018

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