Question

1. a system of equations is shown.

$y = 4x$
$x + y = 5$
which answer correctly shows the first step to solve this system by substitution?
a. $4x = 5$
b. $4x + y = 5$
c. $x + 4x = 5$
d. $y + y = 5$

1. solve the system of equations using the substitution method.

$y = 4x$
$x + y = 5$

1. a system of equations is shown.

$x = -4y$
$3x + 2y = 20$
which answer correctly shows the first step to solve this system by substitution?
a. $3(4y) + 2y = 20$
b. $3(-4y) + 2y = 20$
c. $3x - 4x = 20$
d. $3(-4y) = 20$

1. solve the system of equations using the substitution method.

$x = -4y$
$3x + 2y = 20$

1. a system of equations is shown.

$y = 5x - 8$
$4x + 3y = 33$
which answer correctly shows the first step to solve this system by substitution?
a. $4y + 3y = 33$
b. $4x + 3(5x) = -8$
c. $4x + 5x - 8 = 33$
d. $4x + 3(5x - 8) = 33$

1. solve the system of equations using the substitution method.

$y = 5x - 8$
$4x + 3y = 33$

Explanation:

Question 2

Step1: Identify substitution

We have \( y = 4x \) and \( x + y = 5 \). Substitute \( y = 4x \) into \( x + y = 5 \).

Step2: Perform substitution

Replace \( y \) in \( x + y = 5 \) with \( 4x \), getting \( x + 4x = 5 \). Then solve for \( x \): \( 5x = 5 \), so \( x = 1 \).

Step3: Find y

Substitute \( x = 1 \) into \( y = 4x \), so \( y = 4(1) = 4 \).

Step1: Identify substitution

We have \( x = -4y \) and \( 3x + 2y = 20 \). Substitute \( x = -4y \) into \( 3x + 2y = 20 \).

Step2: Perform substitution

Replace \( x \) in \( 3x + 2y = 20 \) with \( -4y \), getting \( 3(-4y) + 2y = 20 \). Simplify: \( -12y + 2y = 20 \), \( -10y = 20 \), so \( y = -2 \).

Step3: Find x

Substitute \( y = -2 \) into \( x = -4y \), so \( x = -4(-2) = 8 \).

Step1: Identify substitution

We have \( y = 5x - 8 \) and \( 4x + 3y = 33 \). Substitute \( y = 5x - 8 \) into \( 4x + 3y = 33 \).

Step2: Perform substitution

Replace \( y \) in \( 4x + 3y = 33 \) with \( 5x - 8 \), getting \( 4x + 3(5x - 8) = 33 \). Simplify: \( 4x + 15x - 24 = 33 \), \( 19x - 24 = 33 \), \( 19x = 57 \), so \( x = 3 \).

Step3: Find y

Substitute \( x = 3 \) into \( y = 5x - 8 \), so \( y = 5(3) - 8 = 15 - 8 = 7 \).

Answer:

The solution is \( x = 1 \), \( y = 4 \)

Question 4