Question

Choose the system of equations which matches the following graph:

a- x + 2y = −10
3x − y = 12

b- x − 2y = −10
3x − y = 12
c- x + 2y = −10
3x + y = 12
d- x − 2y = −10
3x + y = 12

Answer 1

Option a

- x + 2y = −10

3x − y = 12

Explanation:

step 1

Find the equation of the line with negative slope

we know that

The line with negative slope has a y-intercept at (0,-5) and passes through the point (2,-6)

Find the slope

`m=(-6+5)/(2-0)=-(1)/(2)`

The equation in slope intercept form is

`y=-(1)/(2)x-5`

Convert to standard form

Multiply by 2 both sides

`2y=-x-10\\x+2y=-10`

step 2

Find the equation of the line with positive slope

The line with positive slope has a x-intercept at (4,0) and passes through the point (2,-6)

Find the slope

`m=(-6-0)/(2-4)=3`

The equation of the line in point slope form is equal to

`y-y1=m(x-x1)`

we have

`m=3\\point\ (4,0)`

substitute

`y-0=3(x-4)`

Convert to standard form

`y=3x-12\\3x-y=12`

therefore

The system of equations is

- x + 2y = −10

3x − y = 12