1 Answer

Visual · Answer 1 · 2023-05-12T03:35:52+0000

(-3,4)

Step-by-step explanation

here we have a system of 2 linear functions, To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

so

Step 1

graph the function (1)

a)

to graph the line we need 2 poins, so

i) P1, when x=0

$\begin{gathered} y=-(1)/(3)x+3 \\ y=-(1)/(3)(0)+3=3 \\ so \\ P1=(0,3) \end{gathered}$

ii) P2; when x= 3

$\begin{gathered} y=-(1)/(3)(3)+3=-1+3=2 \\ so \\ P2;\text{ \lparen3,2\rparen} \end{gathered}$

iii) now, draw a line that passes trought P1 and P2

Step 2

now, graph line 2 ( function 2)

i) P3, when x= 0

$\begin{gathered} 3x+y=-5 \\ replace\text{ and solve for y} \\ 3(0)+y=-5 \\ y=5 \\ so,P3=(0,-5) \end{gathered}$

ii) P5, when x= 2

$\begin{gathered} 3x+y=-5 \\ replace\text{ and solve for y} \\ 3(2)+y=-5 \\ 6+y=-5 \\ subtract\text{ 6 in both sides} \\ y=-6-5=-11 \\ y=-11 \\ so,\text{ P4=\lparen2,-11\rparen} \end{gathered}$

iii) now, draw a line that passes trought P3 and P4

Step 3

finally, the solution is the orderede pair where the lines intersect each other

therefore, the solution is

(-3,4)

I hope this helps you