Question

solving equations using substitution
name
solve each system of linear equations using substitution.
$y = 1$
$y = 6x - 11$
$y = 3$
$y = 3x - 27$
$y = 2$
$y = -3x + 5$
$y = 3$
$y = -5x - 17$

Explanation:

First System: \( \boldsymbol{y = 1} \) and \( \boldsymbol{y = 6x - 11} \)

Step1: Substitute \( y = 1 \) into \( y = 6x - 11 \)

\( 1 = 6x - 11 \)

Step2: Solve for \( x \)

Add 11 to both sides: \( 1 + 11 = 6x \) → \( 12 = 6x \)
Divide by 6: \( x = \frac{12}{6} = 2 \)

Step3: Solution is \( (x, y) = (2, 1) \)

\( x = 2 \), \( y = 1 \)

Second System: \( \boldsymbol{y = 3} \) and \( \boldsymbol{y = 3x - 27} \)

Step1: Substitute \( y = 3 \) into \( y = 3x - 27 \)

\( 3 = 3x - 27 \)

Step2: Solve for \( x \)

Add 27 to both sides: \( 3 + 27 = 3x \) → \( 30 = 3x \)
Divide by 3: \( x = \frac{30}{3} = 10 \)

Step3: Solution is \( (x, y) = (10, 3) \)

\( x = 10 \), \( y = 3 \)

Third System: \( \boldsymbol{y = 2} \) and \( \boldsymbol{y = -3x + 5} \)

Step1: Substitute \( y = 2 \) into \( y = -3x + 5 \)

\( 2 = -3x + 5 \)

Step2: Solve for \( x \)

Subtract 5 from both sides: \( 2 - 5 = -3x \) → \( -3 = -3x \)
Divide by -3: \( x = \frac{-3}{-3} = 1 \)

Step3: Solution is \( (x, y) = (1, 2) \)

\( x = 1 \), \( y = 2 \)

Fourth System: \( \boldsymbol{y = 3} \) and \( \boldsymbol{y = -5x - 17} \)

Answer:

s:

1. \( (2, 1) \)
2. \( (10, 3) \)
3. \( (1, 2) \)
4. \( (-4, 3) \)