Question

x+27=14
y=3x-14
and
15x+5y=20
y=8-5x

Answer 1

To solve the system of equations, let's start with the first pair of equations given:

1. \( x + 27 = 14 \)
2. \( y = 3x - 14 \)

**Step 1: Solve for \(x\)**

From the first equation, we can isolate \(x\):

\[
x + 27 = 14 \implies x = 14 - 27 \implies x = -13
\]

**Step 2: Solve for \(y\)**

Now we substitute \(x = -13\) into the second equation to find \(y\):

\[
y = 3(-13) - 14 = -39 - 14 = -53
\]

So from the first pair, we have:

\[
x = -13 \quad \text{and} \quad y = -53
\]

Now let's move on to the second pair of equations:

3. \( 15x + 5y = 20 \)
4. \( y = 8 - 5x \)

**Step 3: Solve the second pair of equations**

We can substitute equation 4 into equation 3:

\[
15x + 5(8 - 5x) = 20
\]

**Step 4: Distributing and solving**

Now we distribute \(5\):

\[
15x + 40 - 25x = 20
\]

Combine like terms:

\[
-10x + 40 = 20
\]

Now, isolate \(x\):

\[
-10x = 20 - 40 \implies -10x = -20 \implies x = 2
\]

**Step 5: Solve for \(y\)**

Now substitute \(x = 2\) back into equation 4 to solve for \(y\):

\[
y = 8 - 5(2) = 8 - 10 = -2
\]

So from the second pair, we have:

\[
x = 2 \quad \text{and} \quad y = -2
\]

**Final Results:**

From the first pair of equations:
- \(x = -13\)
- \(y = -53\)

From the second pair of equations:
- \(x = 2\)
- \(y = -2\)