Question

Solve the system of linear equations by elimination.

-5x + 4y = 28
20z - 16y = -1

a) x=3, y=5, z=-2
b) x=-3, y=-5, z=-2
c) x=-3, y=5, z=-2
d) x=3, y=-5, z=2

Answer 1

To solve the system of linear equations by elimination, multiply the second equation by a suitable number to eliminate one variable. Then, add the two equations and simplify to find the solution.

Step-by-step explanation:

To solve the system of linear equations by elimination, we need to eliminate one variable between the two equations. In the given system:

-5x + 4y = 28

20z - 16y = -1

Multiplying the second equation by 5, we get:

100z - 80y = -5

Now, we can add the two equations:

-5x + 4y + 100z - 80y = 28 - 5

Simplifying the equation:

-5x + 100z - 76y = 23

Rearranging the equation:

-5x - 76y + 100z = 23

So, the solution to the system of equations is:

x = 3, y = -5, z = 2