Question

1. find the solution of the system of equations.

-2x + 7y = 20
x + 7y = 32

1. find the solution of the system of equations.

-10x - 5y = 5
-4x + 5y = 23

1. find the solution of the system of equations.

-5x + 5y = -10
6x + 5y = 1

1. solve the system by substitution.

y = x + 35
y = 8x

1. solve the system by substitution.

y = 4x + 6
y = 7x

1. solve the system by substitution.

y = 9x - 2
y = 7x

Explanation:

Problem 5

Step1: Subtract equations to eliminate $7y$

$(-2x + 7y) - (x + 7y) = 20 - 32$
$-3x = -12$

Step2: Solve for $x$

$x = \frac{-12}{-3} = 4$

Step3: Substitute $x=4$ into $x+7y=32$

$4 + 7y = 32$
$7y = 32 - 4 = 28$
$y = \frac{28}{7} = 4$

Problem 6

Step1: Add equations to eliminate $5y$

$(-10x - 5y) + (-4x + 5y) = 5 + 23$
$-14x = 28$

Step2: Solve for $x$

$x = \frac{28}{-14} = -2$

Step3: Substitute $x=-2$ into $-10x-5y=5$

$-10(-2) - 5y = 5$
$20 - 5y = 5$
$-5y = 5 - 20 = -15$
$y = \frac{-15}{-5} = 3$

Problem 7

Step1: Subtract equations to eliminate $5y$

$(6x + 5y) - (-5x + 5y) = 1 - (-10)$
$11x = 11$

Step2: Solve for $x$

$x = \frac{11}{11} = 1$

Step3: Substitute $x=1$ into $6x+5y=1$

$6(1) + 5y = 1$
$5y = 1 - 6 = -5$
$y = \frac{-5}{5} = -1$

Problem 8

Step1: Substitute $y=8x$ into $y=x+35$

$8x = x + 35$

Step2: Solve for $x$

$8x - x = 35$
$7x = 35$
$x = \frac{35}{7} = 5$

Step3: Solve for $y$

$y = 8(5) = 40$

Problem 9

Step1: Substitute $y=7x$ into $y=4x+6$

$7x = 4x + 6$

Step2: Solve for $x$

$7x - 4x = 6$
$3x = 6$
$x = \frac{6}{3} = 2$

Step3: Solve for $y$

$y = 7(2) = 14$

Problem 10

Step1: Substitute $y=7x$ into $y=9x-2$

$7x = 9x - 2$

Step2: Solve for $x$

$2 = 9x - 7x$
$2x = 2$
$x = \frac{2}{2} = 1$

Step3: Solve for $y$

$y = 7(1) = 7$

Answer:

1. Problem 5: $x=4$, $y=4$
2. Problem 6: $x=-2$, $y=3$
3. Problem 7: $x=1$, $y=-1$
4. Problem 8: $x=5$, $y=40$
5. Problem 9: $x=2$, $y=14$
6. Problem 10: $x=1$, $y=7$