Question

Choose the system of equations which matches the following graph:

x − 2y = 8
2x + 4y = 12


x − 2y = 8
2x − 4y = 12


x + 2y = 8
2x + 4y = 12


x + 2y = 8
2x − 4y = 12

Answer 1

parallel lines...means ur equations will have the same slope and different y int's.

x - 2y = 8....-2y = -x + 8....y = 1/2x - 4...slope is 1/2, y int is -4
2x + 4y = 12...4y = -2x + 12....y = -1/2x + 3...slope is - 1/2, y int is 3
not this one...different slopes

x - 2y = 8...slope is 1/2, y int is -4
2x - 4y = 12...-4y = -2x + 12...y = 1/2x - 3....slope is 1/2, y int is -3
same slope, different y int's.....these are parallel lines..but this is not ur graph because the graph has a negative slope.

x + 2y = 8....2y = -x + 8....y = -1/2x + 4..slope is -1/2, y int is 4
2x + 4y = 12...4y = -2x + 12....y = -1/2x + 3...slope is -1/2, y int is 3
same slope, different y int's...parallel lines...and ur y int's match the graph...this is ur answer <===

x + 2y = 8...slope is -1/2, y int is 4
2x - 4y = 12..slope is 1/2, y int is 3
different slopes, different y int....this has 1 solution and ur lines are not parallel...not this one

therefore, ur answer is : 3rd answer choice

Answer 2

The second and third pairs of the line match the graph.

Line system

It is a one-dimension figure which has no width. It is a combination of infinite points side by side.

Given

1,  x − 2y = 8 and 2x + 4y = 12

2.  x − 2y = 8 and 2x − 4y = 12

3.  x + 2y = 8 and 2x + 4y = 12

4.  x + 2y = 8 and 2x − 4y = 12

To find

Choose the system of equations that matches the following graph.

How do find the system of equations that matches the following graph?

The general form of the line is given by

$\rm a_{1} x + b_{1}y = c_{1}$ and $\rm a_{2} x + b_{2}y = c_{2}$

1.  On comparing with general equation of the line.

$\begin{aligned} a_{1} = 1 \ \ \ &b_{1} = -2 \ \ &c_{1} = 8 \\ a_{2} = 2 \ \ \ &b_{2} = 4 \ \ \ &c_{2} = 12 \\\end{aligned}$

Then $\dfrac{a_{1} }{a_{2} } \neq \dfrac{b_{1} }{b_{2} }$

hence this is the condition for the intersecting line.

2.  On comparing with general equation of the line.

$\begin{aligned} a_{1} = 1 \ \ \ &b_{1} = -2 \ \ &c_{1} = 8 \\ a_{2} = 2 \ \ \ &b_{2} = -4 \ \ \ &c_{2} = 12 \\\end{aligned}$

Then $\dfrac{a_{1} }{a_{2} } = \dfrac{b_{1} }{b_{2} } \neq \dfrac{c_{1} }{c_{2} }$

hence this is the condition for the Parallel line.

3.  On comparing with general equation of the line.

$\begin{aligned} a_{1} = 1 \ \ \ &b_{1} = 2 \ \ &c_{1} = 8 \\ a_{2} = 2 \ \ \ &b_{2} = 4 \ \ \ &c_{2} = 12 \\\end{aligned}$

Then $\dfrac{a_{1} }{a_{2} } = \dfrac{b_{1} }{b_{2} } \neq \dfrac{c_{1} }{c_{2} }$

hence this is the condition for the Parallel line.

4.  On comparing with general equation of the line.

$\begin{aligned} a_{1} = 1 \ \ \ &b_{1} = 2 \ \ &c_{1} = 8 \\ a_{2} = 2 \ \ \ &b_{2} = -4 \ \ \ &c_{2} = 12 \\\end{aligned}$

Then $\dfrac{a_{1} }{a_{2} } \neq \dfrac{b_{1} }{b_{2} }$

hence this is the condition for the intersecting line.

Thus the second and third pairs of the line match the graph.

More about the line system link is given below.

https://brainly.com/question/2696693