Answer:
[tex]a=3\\b=1[/tex]
Step-by-step explanation:
[tex]9a+3b=30\\8a+4b=28[/tex]
Let's solve the second equation for a to later on replace it in the first equation.
[tex]8a+4b=28\\8a=28-4b\\a=\frac{28-4b}{8}[/tex]
Now plug this into the first equation.
[tex]9a+3b=30\\9(\frac{28-4b}{8})+3b=30[/tex]
Distribute the 9
[tex](\frac{252-36b}{8}) +3b=30[/tex]
Break down the fraction.
[tex]\frac{252}{8}-\frac{36b}{8}+3b=30[/tex]
Simplify.
[tex]\frac{63}{2}-\frac{9}{2}b+3b=30[/tex]
Subtract [tex]\frac{63}{2}[/tex]
[tex]-\frac{9}{2}b+3b=30-\frac{63}{2}[/tex]
Combine like terms.
[tex]\frac{-9+2*3}{2}b=\frac{30*2-63}{2}[/tex]
[tex]\frac{-9+6}{2}b=\frac{60-63}{2}[/tex]
[tex]\frac{-3}{2}b=\frac{-3}{2}[/tex]
Muliply by the reciprocal or inverted fraction next to b.
[tex](-\frac{2}{3})(-\frac{3}{2}) b=-\frac{3}{2}(-\frac{2}{3})[/tex]
[tex]b=1[/tex]
Now plug this value into any of the equations to find the value of a.
[tex]8a+4b=28\\8a+4(1)=28\\8a+4=28\\8a=28-4\\8a=24\\a=\frac{24}{8}\\ a=3[/tex]
