Question

#1 x = 8
3x + 4y = 16
#2 y = 3x + 4
y = 8x + 4
#3 2x + 3y = 21
y = -x + 3
#4 x = 2y - 7
x = y - 4
student teachers only (hint: solve for y in the first equation).
#5 4x - y = 10
2x = 12 - 3y

Explanation:

#1

Step1: Substitute \( x = 8 \) into \( 3x + 4y = 16 \)

\( 3\times8 + 4y = 16 \)
\( 24 + 4y = 16 \)

Step2: Solve for \( y \)

Subtract 24 from both sides: \( 4y = 16 - 24 = -8 \)
Divide by 4: \( y = \frac{-8}{4} = -2 \)

Step1: Set the two equations equal (since both equal \( y \))

\( 3x + 4 = 8x + 4 \)

Step2: Solve for \( x \)

Subtract \( 3x \) and 4 from both sides: \( 0 = 5x \) so \( x = 0 \)

Step3: Substitute \( x = 0 \) into \( y = 3x + 4 \)

\( y = 3\times0 + 4 = 4 \)

Step1: Substitute \( y = -x + 3 \) into \( 2x + 3y = 21 \)

\( 2x + 3(-x + 3) = 21 \)
\( 2x - 3x + 9 = 21 \)

Step2: Solve for \( x \)

Combine like terms: \( -x + 9 = 21 \)
Subtract 9: \( -x = 12 \) so \( x = -12 \)

Step3: Substitute \( x = -12 \) into \( y = -x + 3 \)

\( y = -(-12) + 3 = 12 + 3 = 15 \)

Answer:

\( x = 8, y = -2 \)

#2