Answer:
1. Option 4.
2. Option 1.
3. Option 3.
Step-by-step explanation:
1.
The given point is (3, −6), we need to find the graph that shows a pair of lines that represents the equations with the solution (3, −6).
In point (3,-6), the x-coordinate is positive and y-coordinate is negative.
It means a pair of lines is shown intersecting on ordered pair 3 units to the right and 6 units down.
Therefore, the correct option is 4.
2.
Given equations are
[tex]m+3n=10[/tex] .... (1)
[tex]m=n-2[/tex] ..... (2)
Substitute the value of m from equation (2) in equation (1).
[tex](n-2)+3n=10[/tex]
[tex]4n-2=10[/tex]
[tex]4n=10+2[/tex]
[tex]4n=12[/tex]
[tex]n=3[/tex]
Substitute n=3 in equation (2).
[tex]m=3-2=1[/tex]
The solution to the set of equations in the form (m, n) is (1,3).
Therefore, the correct option is 1.
3.
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
It is given that first line passes through the points (3,0) and (0,6). So, the equation of line is
[tex]y-0=\frac{6-0}{0-3}(x-3)[/tex]
[tex]y=-2(x-3)[/tex]
[tex]y=-2x+6[/tex]
It is given that first line passes through the points (0,0) and (5,5). So, the equation of line is
[tex]y-0=\frac{5-0}{5-0}(x-0)[/tex]
[tex]y=x[/tex]
Two equation are [tex]y=-2x+6[/tex] and [tex]y=x[/tex]. Find the values of both function at x=0 adn x=2.
At x=0,
[tex]y=-2(0)+6=6[/tex] and [tex]y=0[/tex].
At x=2,
[tex]y=-2(2)+6=2[/tex] and [tex]y=2[/tex].
(0,6) is the solution to line A but not to line B.
(2, 2) is the solution to both lines A and B.
Therefore, the correct option is 3.
