Answer: C. The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
Step-by-step explanation:
You know that the first equation is:
[tex]-3x-8=19[/tex]
And the second equation is:
[tex]-3x-2=25[/tex]
According to the Addition property of equality:
If [tex]a=b[/tex]; then [tex]a+c=b+c[/tex]
Then, you can add 6 to both sides of the first equation to keep it balanced. Then, you get:
[tex]-3x-8=19\\\\-3x-8+(6)=19+(6)[/tex]
[tex]-3x-2=25[/tex]
Therefore, you can observe that the second equation can be obtained by adding 6 to both sides of the first equation, therefore, the equations have the same solution.
If you want to verify this, you can solve for "x" from both equations:
- First equation:
[tex]-3x-8=19\\\\-3x=19+8\\\\x=\frac{27}{-3}\\\\x=-9[/tex]
- Second equation:
[tex]-3x-2=25\\\\-3x=25+2\\\\x=\frac{27}{-3}\\\\x=-9[/tex]
