Question

Solve using elimination method
8y+4z=7
6y-8z=41

Answer 1

To solve the system of equations using the elimination method, we need to eliminate either y or z in one of the equations. In this case, we can eliminate y by multiplying the first equation by 3 and the second equation by 4:

3(8y + 4z) = 3(7)
4(6y - 8z) = 4(41)

Simplifying:

24y + 12z = 21
24y - 32z = 164

Next, subtract the second equation from the first equation to eliminate y:

(24y + 12z) - (24y - 32z) = 21 - 164
24y + 12z - 24y + 32z = 21 - 164
44z = -143

Now solve for z:

z = -143/44

Simplifying the result:

z = -3.25

Now substitute the value of z back into either original equation to solve for y. Using the first equation:

8y + 4z = 7
8y + 4(-3.25) = 7
8y - 13 = 7
8y = 20
y = 20/8
y = 2.5

Therefore, the solution to the system of equations is y = 2.5 and z = -3.25.