Question

Choose the system of equations which matches the following graph: (1 point) a line includes points 0 comma negative 1 and 5 comma negative 2. A line includes points 5 comma negative 2 and 0 comma negative 5 3x + 5y = −25 x−5y = 5 3x + 5y = −25 x + 5y =−5 3x − 5y = 25 x + 5y =−5 3x − 5y = 25 x−5y = 5

Answer 1

Answer:

The system of equations is

$x+5y=-5$

$3x-5y=25$

Step-by-step explanation:

step 1

Find the equation of a line that passes through the points

(0,-1) and (5,-2)

Find the slope

$m=(-2+1)/(5-0)=-\frac{1}{5}$

The equation of the line in slope intercept form is

$y=mx+b$

we have

$m=-\frac{1}{5}$

$b=-1$ ---> the y-intercept is given

substitute

$y=-\frac{1}{5}x-1$

Convert to standard form

Multiply by 5 both sides

$5y=-x-5$

$x+5y=-5$ ----> equation 1

step 2

Find the equation of a line that passes through the points

(5,-2) and (0,-5)

Find the slope

$m=(-5+2)/(0-5)=\frac{3}{5}$

The equation of the line in slope intercept form is

$y=mx+b$

we have

$m=\frac{3}{5}$

$b=-5$ ---> the y-intercept is given

substitute

$y=\frac{3}{5}x-5$

Convert to standard form

Multiply by 5 both sides

$5y=3x-25$

$3x-5y=25$ ----> equation 2

therefore

The system of equations is

$x+5y=-5$

$3x-5y=25$

The solution of the system is the point (5,-2)

Because is a common point both graphs