The solution is [tex](x=\frac{-7}{2},\ y=\frac{-13}{2} )[/tex].
Solution:
Given system of equations are
[tex]-3 x+y=4[/tex] ---------- (1)
[tex]-9 x+5 y=-1[/tex] ---------- (2)
To solve the given system of equations by substitution method.
Let us take the equation (1) and find the value of y.
(1) ⇒ [tex]-3 x+y=4[/tex]
Add 3x on both sides of the equation, we get
⇒ [tex]y=4+3x[/tex]
Substitute y = 4 + 3x in equation (2), we get
[tex]-9 x+5 (4+3x)=-1[/tex]
[tex]-9 x+20+15x=-1[/tex]
Combine like terms together.
[tex]-9 x+15x=-1-20[/tex]
[tex]6x=-21[/tex]
Divide by 6 on both sides of the equation.
[tex]$x=-\frac{21}{6}[/tex]
Divide the numerator and denominator by the common factor 3.
[tex]$x=-\frac{21\div3}{6\div3}[/tex]
[tex]$x=-\frac{7}{2}[/tex]
Now, substitute x value in y = 4 + 3x, we get
[tex]$y=4+3\left(\frac{-7}{2} \right)[/tex]
[tex]$y=4+\left(\frac{-21}{2} \right)[/tex]
Take LCM of the denominators and make the same.
[tex]$y=\frac{8}{2} +\frac{-21}{2}[/tex]
[tex]$y=\frac{-13}{2}[/tex]
Hence the solution is [tex](x=\frac{-7}{2},\ y=\frac{-13}{2} )[/tex].
