Question

Find the points of intersection of the lines 10x−4y=2 and 2x+8y=7 without graphing.

Answer 1

Answer:

$x=\frac{1}{2},y=\frac{3}{4}$

Step-by-step explanation:

Given:

$10x-4y=2 ,2x+8y=7$

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.

$10x-4y=2 \\2(5x-2y)=2\\5x-2y=1\\5x=1+2y\\x=\frac{1+2y}{5}$

Put $x=\frac{1+2y}{5}$ in the equation $2x+8y=7$

$2x+8y=7\\2[\frac{1+2y}{5}]+8y=7\\ 2+4y+40y=35\\44y=35-2\\44y=33\\y=\frac{33}{44}\\ =\frac{3}{4}$

Put $y=\frac{3}{4}$ in the equation $x=\frac{1+2y}{5}$

$x=\frac{1+2y}{5}\\=\frac{1}{5}[1+2(\frac{3}{4})]\\=\frac{1}{5}[1+(\frac{3}{2})]\\\\=\frac{1}{5}(\frac{2+3}{2}) \\\\=\frac{1}{5}(\frac{5}{2})\\\\=\frac{1}{2}$

Therefore,

$x=\frac{1}{2},y=\frac{3}{4}$