Question

solve each system by substitution.

1. ( y = 7x )

( -5x - 3y = 0 )

1. ( 16x - 2y = 5 )

( y = 8x )

1. ( -2(3n + 3) + n = -10 - 5n )
2. ( -5 - (4p - 7) = 2 - 4p )

Explanation:

Problem 9

Step1: Expand left-hand side

$-6n - 6 + n = -10 - 5n$

Step2: Combine like terms

$-5n - 6 = -10 - 5n$

Step3: Add $5n$ to both sides

$-6 = -10$

Problem 10

Step1: Expand left-hand side

$-5 - 4p + 7 = 2 - 4p$

Step2: Combine like terms

$-4p + 2 = 2 - 4p$

Step3: Add $4p$ to both sides

$2 = 2$

Problem 11

Step1: Substitute $y=7x$ into equation

$-5x - 3(7x) = 0$

Step2: Simplify the equation

$-5x - 21x = 0 \implies -26x = 0$

Step3: Solve for $x$

$x = 0$

Step4: Solve for $y$

$y = 7(0) = 0$

Problem 12

Step1: Substitute $y=8x$ into equation

$16x - 2(8x) = 5$

Step2: Simplify the equation

$16x - 16x = 5 \implies 0 = 5$

Answer:

1. No solution (contradiction, $-6

eq -10$)

1. Infinitely many solutions (identity, $2=2$)
2. $x=0$, $y=0$
3. No solution (contradiction, $0

eq 5$)