Question

Solve the simultaneous equation 8y+4z=7
6y-8z=41 with elimination method

Answer 1

To solve the simultaneous equations using the elimination method, we have the following two equations:

1) \( 8y + 4z = 7 \)
2) \( 6y - 8z = 41 \)

**Step 1: Align the equations for elimination**

Let's first manipulate the equations to eliminate one of the variables. We can multiply both equations by suitable constants to make the coefficients of one variable the same.

We'll eliminate \( z \). Since the coefficients of \( z \) in the two equations are \( 4 \) and \( -8 \), we can multiply the first equation by \( 2 \) to match the coefficients of \( z \):

Multiplying the first equation by \( 2 \):

\( 2(8y + 4z) = 2(7) \)
\( 16y + 8z = 14 \) (Equation 3)

Now we have:

3) \( 16y + 8z = 14 \)
4) \( 6y - 8z = 41 \)

**Step 2: Add equations (3) and (4)**

Now we can add Equation 3 and Equation 4 together:

\[
(16y + 8z) + (6y - 8z) = 14 + 41
\]
\[
16y + 6y + 8z - 8z = 55
\]
\[
22y = 55
\]

**Step 3: Solve for \( y \)**

\[
y = \frac{55}{22}
\]
\[
y = 2.5
\]

**Step 4: Substitute \( y \) back into one of the original equations**

Now we substitute \( y = 2.5 \) back into one of the original equations. We'll use the first equation:

\[
8y + 4z = 7
\]
Substituting \( y = 2.5 \):

\[
8(2.5) + 4z = 7
\]
\[
20 + 4z = 7
\]
\[
4z = 7 - 20
\]
\[
4z = -13
\]
\[
z = \frac{-13}{4}
\]
\[
z = -3.25
\]

**Final Solution:**
The solution to the simultaneous equations is:

\[
y = 2.5, \quad z = -3.25
\]

Feel free to ask if you have any follow-up questions!