Answer:
[tex]\left\{\begin{array}{ccc}(A+L)x+(B+M)y=C+N\\Ax+By=C\end{array}\right[/tex]
Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}Ax+By=C\\Lx+My=N\end{array}\right}\qquad\text{add both sides of the equations}\\(Ax+Lx)+(By+My)=C+N\qquad\text{distributive}\\(A+L)x+(B+M)y=C+N[/tex]
Equivalent expressions are expressions that have the same value.
The true statement is: (a) The first equation in System 2 is the sum of the equations in System 1. The second equation in System 2 is the first equation in System 1.
The systems of equations are:
System 1
[tex]\mathbf{Ax + By = C}[/tex]
[tex]\mathbf{Lx + My = N}[/tex]
System 2
[tex]\mathbf{(A + L)x + (8 + M)y = C + N}[/tex]
[tex]\mathbf{Ax + By = C}[/tex]
When the equations of system 1 are added, we have:
[tex]\mathbf{Ax + Lx + By + My = C + D}[/tex]
Factor out x and y
[tex]\mathbf{(A + L)x + (8 + M)y = C + N}[/tex]
The above equation is the first equation of system 2.
While [tex]\mathbf{Ax + By = C}[/tex] is the second equation of the system
Hence, the true statement is (a)
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