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Use the system of equations and graphs below to complete the sentence.
x - 2y = 5
3x + 15y = -6
The graph that correctly represents the given system of equations is a graph ( ), and the solution to the system is ( , ).
The correct option will be Option B: Graph B and the solution of the given system of equations will be (3,-1).
Given the first equation is x-2y=5
in this equation of line, the x-coordinate is:
x-(2.0)=5
⇒ x=5
The x-coordinate will be (5,0).
in this equation of line, the y-coordinate is:
0- 2y=5
⇒y= -5/2
The y-coordinate will be (0,-5/2).
So the first line equation has x-coordinate (5,0) and y-coordinate (0,-5/2).
Similarly,
Given the second equation is 3x+15y=-6
in this equation of line, the x-coordinate is:
3x+(15.0)=-6
⇒ x=6/3=2
The x-coordinate will be (2,0).
in this equation of line, the y-coordinate is:
(3.0)+15y=-6
⇒y= -6/15= -2/5
The y-coordinate will be (0,-2/5).
So the second line equation has x-coordinate (2,0) and y-coordinate (0,-2/5).
Equation-1: x - 2y = 5
⇒x =2y+5
putting the value of x in equation-2
3x + 15y = -6
⇒ 3(2y+5)+15y=-6
⇒6y+15+15y=-6
⇒21y=-6-15=-21
⇒y=-21/21=-1
putting the value of y in equation of x
x= 2(-1)+5= -2+5= 3
The solution of system of equations will be (3,-1)
Checking all the options
In option B one line has x-coordinate (5,0) and y-coordinate (0,-5/2) and another line has x-coordinate (2,0) and y-coordinate (0,-2/5).
And the point of intersection of two lines is (3,-1).
Therefore the correct option will be Option B: Graph B and the solution of the given system of equations will be (3,-1).
Learn more about the system of equations
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