Respuesta :
Answer:
[tex]x=\frac{1}{2},y=\frac{3}{4}[/tex]
Step-by-step explanation:
Given:
[tex]10x-4y=2 ,2x+8y=7[/tex]
To find: points of intersection of the given lines
Solution:
In substitution method, the system of equations is solved by expressing one variable in terms of another, as a result, removing one variable from an equation.
[tex]10x-4y=2 \\2(5x-2y)=2\\5x-2y=1\\5x=1+2y\\x=\frac{1+2y}{5}[/tex]
Put [tex]x=\frac{1+2y}{5}[/tex] in the equation [tex]2x+8y=7[/tex]
[tex]2x+8y=7\\2[\frac{1+2y}{5}]+8y=7\\ 2+4y+40y=35\\44y=35-2\\44y=33\\y=\frac{33}{44}\\ =\frac{3}{4}[/tex]
Put [tex]y=\frac{3}{4}[/tex] in the equation [tex]x=\frac{1+2y}{5}[/tex]
[tex]x=\frac{1+2y}{5}\\=\frac{1}{5}[1+2(\frac{3}{4})]\\=\frac{1}{5}[1+(\frac{3}{2})]\\\\=\frac{1}{5}(\frac{2+3}{2}) \\\\=\frac{1}{5}(\frac{5}{2})\\\\=\frac{1}{2}[/tex]
Therefore,
[tex]x=\frac{1}{2},y=\frac{3}{4}[/tex]
