The solution of the system of equations is a = 4 and b = 5.
What is the system of equations?
A system of equations is a set of two or more equations that you deal with at one time.
The given system of equations are;
8a + 12b = 92
6a – 4b = 4
From equation 1
[tex]\rm 8a + 12b = 92\\\\ 8a=92-12b\\\\a=\dfrac{92-12b}{8}[/tex]
Substitute the value of a in the equation 2
[tex]\rm 6a-4b=4\\\\6\times \dfrac{92-12b}{8}-4b=4\\\\3\times \dfrac{92-12b}{4}-4b=4\\\\ 276-36b-16b=16\\\\-52b=16-276\\\\-52b=-260\\\\b=\dfrac{-260}{-52}\\\\b=5[/tex]
Substitute the value of b in the equation 2
[tex]\rm 6a – 4b = 4\\\\6a-4\times 5=4\\\\6a-20=4\\\\6a=4+20\\\\6a=24\\\\a=\dfrac{24}{6}\\\\a=4[/tex]
Hence, the solution of the system of equations is a = 4 and b = 5.
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