Answer:x = 1; y = 1Step-by-step explanation:First thing we will do is work with the first equation: [tex]4x - 3y = 1[/tex][tex]4x = 1+3y[/tex][tex]x = \frac{3}{4} y~+~\frac{1}{4}[/tex]Now that we have a value for x, we insert that into the second equation, like so:[tex]5(\frac{3}{4}y~+~\frac{1}{4}) + 4y = 9[/tex][tex]\frac{15}{4}y~+~\frac{5}{4} + 4y = 9[/tex][tex]\frac{15}{4}y~+~4y~+~\frac{5}{4} = 9[/tex][tex]\frac{15}{4}y~+~\frac{16}{4} y~+~\frac{5}{4}[/tex][tex]\frac{31}{4}y~+~\frac{5}{4} =9[/tex][tex]31y + 5 = 9 * 4[/tex][tex]31y + 5 = 36[/tex][tex]31y = 36-5[/tex][tex]31y = 31[/tex][tex]y = \frac{31}{31}[/tex][tex]y = 1[/tex]Now, we solve for x:[tex]4x - 3(1) = 1[/tex][tex]4x - 3 = 1[/tex][tex]4x = 1 + 3[/tex][tex]4x = 4[/tex][tex]x = \frac{4}{4}[/tex][tex]x=1[/tex]Hope it helped,BiologiaMagister