Question

finding poi using substitution
find the poi of the two equations:
$y = x + 4$
$2x + y = 16$
step 1 plug the first equation $y = x + 4$ into the second equation $2x + y = 16$.
step 2 rearrange equation to isolate $x$ (solve for $x$).

Explanation:

Step 1: Substitute \( y = x + 4 \) into \( 2x + y = 16 \)

We know \( y = x + 4 \), so replace \( y \) in the second equation with \( x + 4 \).
\( 2x + (x + 4) = 16 \)
Simplify the left - hand side: \( 2x+x + 4=16\), which is \( 3x+4 = 16 \)

Step 2: Solve for \( x \)

Subtract 4 from both sides of the equation \( 3x + 4=16 \):
\( 3x+4 - 4=16 - 4 \)
\( 3x=12 \)
Divide both sides by 3: \( x=\frac{12}{3}=4 \)

Step 3: Solve for \( y \)

Substitute \( x = 4 \) into the first equation \( y=x + 4 \)
\( y=4 + 4=8 \)

Answer:

The point of intersection (POI) is \( (4,8) \)