The coordinates of R is [tex]R(0,\frac{23}{11})[/tex].
The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.
Given
The line segment joining P(-6,7) and Q(5,-2) intersects the y-axis at the point R.
Suppose y = kx + b, through point P(-6,7) and Q(5,-2).
7 = -6k + b........(1)
-2 = 5k + b........(2)
By using elimination method
Equation 1 - Equation 2
⇒ 7- (-2)=(-6k + b) - (5k + b)
⇒ 9= -6k -5k + b - b
⇒ 9 = -11k
⇒ [tex]k=-\frac{9}{11}[/tex]
Substitute [tex]k=-\frac{9}{11}[/tex] in equation 1
⇒ [tex]7=-6(-\frac{9}{11} )+b[/tex]
⇒ [tex]b =7-\frac{54}{11}[/tex]
⇒ [tex]b =\frac{77-54}{11}[/tex]
⇒ [tex]b =\frac{23}{11}[/tex]
Thus, [tex]y=-\frac{9}{11}x +\frac{23}{11}[/tex]
Let x = 0, [tex]y = \frac{23}{11}[/tex]
So, [tex]R(0,\frac{23}{11})[/tex]
The coordinates of R is [tex]R(0,\frac{23}{11})[/tex].
Find out more information about elimination method here
brainly.com/question/14619835
#SPJ2
