Answer:
1). Other line is, y = [tex]\frac{1}{3}x+5[/tex]
2). Solution of the system is (3, 6)
Step-by-step explanation:
From the table (1),
Let the equation of the line from the given table is,
y - y' = m(x - x')
Where m = slope of the line
(x', y') is a point lying on the line.
Choose two points from the table which lie on the line.
Let the points are (0, 5) and (3, 6)
Slope = m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
= [tex]\frac{5-6}{0-3}[/tex]
= [tex]\frac{1}{3}[/tex]
Therefore, equation of the will be,
y - 5 = [tex]\frac{1}{3}(x-0)[/tex]
y = [tex]\frac{1}{3}x+5[/tex] -------(1)
Let the other line from the table (2) is,
y - y" = m'(x - x")
Two points taken from this table are (0, 7) and (3, 6)
m' = [tex]\frac{7-6}{0-3}[/tex]
= [tex]-\frac{1}{3}[/tex]
Equation of the line will be,
y - 7 = [tex]-\frac{1}{3}(x-0)[/tex]
y = [tex]-\frac{1}{3}x+7[/tex] -------(2)
Therefore, equation of the other line will be, y = [tex]\frac{1}{3}x+5[/tex]
By adding equations (1) and (2),
y + y = [tex]-\frac{1}{3}x+\frac{1}{3}x+5+7[/tex]
2y = 12
y = 6
From equation (1),
6 = [tex]\frac{1}{3}x+5[/tex]
[tex]\frac{1}{3}x=7-6[/tex]
x = 3
Therefore, solution of the system is (3, 6).
