Answer:
Option a
- x + 2y = −10
3x − y = 12
Step-by-step 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
[tex]m=(-6+5)/(2-0)=-\frac{1}{2}[/tex]
The equation in slope intercept form is
[tex]y=-\frac{1}{2}x-5[/tex]
Convert to standard form
Multiply by 2 both sides
[tex]2y=-x-10\\x+2y=-10[/tex]
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
[tex]m=(-6-0)/(2-4)=3[/tex]
The equation of the line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=3\\point\ (4,0)[/tex]
substitute
[tex]y-0=3(x-4)[/tex]
Convert to standard form
[tex]y=3x-12\\3x-y=12[/tex]
therefore
The system of equations is
- x + 2y = −10
3x − y = 12
