Answer:
The correct options are 3 and 4.
Step-by-step explanation:
An equation in the system is
[tex]y=x+1[/tex]
The only one solution of the system of equation is (0,1). It means the equation must be satisfied by the point (0,1) and the equation is not equivalent to the given equation.
Two equations [tex]a_1x+b_1y+c_1=0[/tex] and [tex]a_2x+b_2y+c_2=0[/tex] are equivalent if
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
All the given equations are not equivalent equations because for all equation
s
[tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
Check each equation by (0,1).
For equation 1,
[tex]x-y=1[/tex]
[tex]0-1=1[/tex]
[tex]-1=1[/tex]
This statement is false, therefore the option 1 is incorrect.
For equation 2,
[tex]2x+2y=4[/tex]
[tex]2(0)+2(1)=4[/tex]
[tex]2=4[/tex]
This statement is false, therefore the option 2 is incorrect.
For equation 3,
[tex]x+y=1[/tex]
[tex]0+1=1[/tex]
[tex]1=1[/tex]
This statement is true, therefore the option 3 is correct.
For equation 4,
[tex]x+2y=2[/tex]
[tex]0+2(1)=2[/tex]
[tex]2=2[/tex]
This statement is true, therefore the option 4 is correct.
