Part(A):
To solve the system of Linear equations using Substitution:
[tex] x+y=7 \\ 2x+y=5 [/tex]
Consider the first equation, x+y=7 implies x=7-y
[tex] \mathrm{Subsititute\:}x=7-y [/tex]
[tex] 2\left(7-y\right)+y=5 [/tex]
[tex] 14-2y+y=5 [/tex]
[tex] 14-y=5 [/tex]
[tex] \mathrm{Subtract\:}14\mathrm{\:from\:both\:sides} [/tex]
[tex] 14-y-14=5-14 [/tex]
[tex] -y=-9 [/tex]
[tex] \mathrm{Divide\:both\:sides\:by\:}-1 [/tex]
[tex] y=9 [/tex]
[tex] \mathrm{For\:}x=7-y [/tex]
[tex] \mathrm{Subsititute\:}y=9 [/tex]
[tex] x=7-9=-2. [/tex][tex] \mathrm{The\:solutions\:to\:the\:system\:of\:equationts\:are:} [/tex]
[tex] y=9,\:x=-2 [/tex]
PArt(B): Use a graph to verify your answer to the system:
Using Desmos graphing calculator, graph the two equations.
