Given:
The given system of equation is:
[tex]y=-2x+1[/tex]
[tex]4x+2y=-3[/tex]
To find:
The solution of given system of equations using subtraction.
Solution:
We have,
[tex]y=-2x+1[/tex] ...(i)
[tex]4x+2y=-3[/tex] ...(ii)
First equation can be rewritten as
[tex]2x+y=1[/tex] (Adding 2x on both sides)
[tex]4x+2y=2[/tex] ...(iii) (Multiplying both sides by 2)
After subtracting (ii) from (iii), we get
[tex]4x+2y-(4x+2y)=2-(-3)[/tex]
[tex]4x+2y-4x-2y=2+3[/tex]
[tex]0=5[/tex]
This statement is false because [tex]0\neq 5[/tex]. It means, there is no value of x and y for which the given system of equations are true.
Therefore, the given system of equations has no solution and the correct option is b.
