Answer:
[tex]x=4,\:y=-49[/tex]
Step-by-step explanation:
we are given with two linear equations and asked to solve them for x and y .
We will solve them by substitution method.
Given that
[tex]y=-10x-9[/tex]
We replace this value of y in second equation that is
[tex]7x+5y=-217[/tex]
[tex]\mathrm{Subsititute\:}y=-10x-9[/tex]
[tex]7x+5\left(-10x-9\right)=-217[/tex]
[tex]7x-50x-45=-217[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:7x-50x=-43x[/tex]
[tex]-43x-45=-217[/tex]
[tex]\mathrm{Add\:}45\mathrm{\:to\:both\:sides}[/tex]
[tex]-43x=-172[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-43[/tex]
[tex]x=4[/tex]
[tex]\mathrm{For\:}y=-10x-9[/tex]
[tex]\mathrm{Subsititute\:}x=4[/tex]
[tex]y=-10\cdot \:4-9[/tex]
[tex]y=-49[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=4,\:y=-49[/tex]
