Question

drag each system of equations to the correct location on the table.
classify each system of equations as having a single solution, no solution, or infinite solutions.

table columns: single solution, no solution, infinite solutions

options:

1. \\(\

$$\begin{aligned} y &= 5 - 2x \\\\ 4x + 2y &= 10 \\end{aligned}$$

\\)

1. \\(\

$$\begin{aligned} x &= 26 - 3y \\\\ 2x + 6y &= 22 \\end{aligned}$$

\\)

1. \\(\

$$\begin{aligned} 5x + 4y &= 6 \\\\ 10x - 2y &= 7 \\end{aligned}$$

\\)

1. \\(\

$$\begin{aligned} x + 2y &= 3 \\\\ 4x + 8y &= 15 \\end{aligned}$$

\\)

1. \\(\

$$\begin{aligned} 3x + 4y &= 17 \\\\ -6x &= 10y - 39 \\end{aligned}$$

\\)

1. \\(\

$$\begin{aligned} x + 5y &= 24 \\\\ 5x &= 12 - y \\end{aligned}$$

\\)

Explanation:

Analyze the first system

Using the Systems of Linear Equations and Number of Solutions knowledge points

$$
LATEXBLOCK0
$$

Analyze the second system

Using the Systems of Linear Equations and Number of Solutions knowledge points

$$
LATEXBLOCK1
$$

Analyze the third system

Using the Systems of Linear Equations and Number of Solutions knowledge points

$$
LATEXBLOCK2
$$

Analyze the fourth system

Using the Systems of Linear Equations and Number of Solutions knowledge points

$$
LATEXBLOCK3
$$

Analyze the fifth and sixth systems

Using the Systems of Linear Equations and Number of Solutions knowledge points

$$
LATEXBLOCK4
$$

Answer:

Single Solution	No Solution	Infinite Solutions

| \(

$$\begin{cases} 5x + 4y = 6 \\ 10x - 2y = 7 \end{cases}$$

\) | \(

$$\begin{cases} x = 26 - 3y \\ 2x + 6y = 22 \end{cases}$$

\) | \(

$$\begin{cases} y = 5 - 2x \\ 4x + 2y = 10 \end{cases}$$

\) |
| \(

$$\begin{cases} 3x + 4y = 17 \\ -6x = 10y - 39 \end{cases}$$

\) | \(

$$\begin{cases} x + 2y = 3 \\ 4x + 8y = 15 \end{cases}$$

\) | |
| \(

$$\begin{cases} x + 5y = 24 \\ 5x = 12 - y \end{cases}$$

\) | | |