solve the equation through elimination:8y+4z=7 and 6y - 8z =41
solve the elimination method 8y+4z=7 and 6y-8z=41
8y+4z=7
6y-8z=41
Multiply eqn 1 by 2 and equn 2 by 1 and add to eliminate z. Solve
To solve the system of equations using the method of elimination, follow these steps:
Step 1: Multiply each equation by suitable coefficients to make the coefficients of either y or z the same in both equations.
Given equations:
1) 8y + 4z = 7
2) 6y - 8z = 41
We can start by multiplying equation 1 by 2 and equation 2 by 4 to make the coefficients of z the same in both equations.
Equation 1: 2(8y + 4z) = 2(7)
Simplifying, we get: 16y + 8z = 14
Equation 2: 4(6y - 8z) = 4(41)
Simplifying, we get: 24y - 32z = 164
Now we have two equations with the same coefficient for z.
Step 2: Add or subtract the equations to eliminate one variable.
Now we can subtract equation 2 from equation 1 to eliminate z.
(16y + 8z) - (24y - 32z) = 14 - 164
16y + 8z - 24y + 32z = -150
-8y + 40z = -150
Step 3: Solve the resulting equation.
To solve for y, divide through by -8:
(-8y + 40z) / -8 = -150 / -8
y - 5z = 18.75
So, the simplified equation after elimination is y - 5z = 18.75.
This equation will help you find the relationship between y and z in the given system of equations.