Answer:
x = 1; y = 1
Step-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
