First step is to write one equation as one variable in terms of another variable.
From the given, we have two equations :
Equation 1 :
3x + 5y = 2
Equation 2 :
x + 3y = 4
Rewrite Equation 2 as the step above.
[tex]\begin{gathered} x+3y=4 \\ x=4-3y \end{gathered}[/tex]2nd step is to substitute the resulting equation to Equation 1 :
[tex]\begin{gathered} 3x+5y=2 \\ 3(4-3y)+5y=2 \\ 12-9y+5y=2 \\ -4y=2-12 \\ -4y=-10 \\ y=\frac{-10}{-4}=\frac{5}{2} \end{gathered}[/tex]3rd step is to substitute this y value to Equation 2 :
[tex]\begin{gathered} x=4-3y \\ x=4-3(\frac{5}{2}) \\ x=4-\frac{15}{2} \\ x=-\frac{7}{2} \end{gathered}[/tex]The intersection is at (x, y)
The answer is (-7/2, 5/2)
