Question

$solve \: \: \: subtitiution \: \: \: method \\ \\ x - 2y = 5 \\ 2x + 3y = 10$
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Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf x - 2y = 5 - (1)$

$\sf 2x + 3y = 10 - (2)$

step by step explanation

1. First we find value of x from Equation 1
2. After finding X substitute/place this value in Equation 2 so that another value comes e.g,value of y.
3. After finding y's value again put this value in equation 1 to find x

From Equation 1

$\sf \bold{\: x = 5 + 2y - (3)}$

Put x into Equation 2

$\sf \longmapsto2x + 3y = 10$

$\sf \longmapsto2(5 + 2y) + 3y = 10$

$\sf \longmapsto10 + 4y + 3y = 10$

$\sf \longmapsto10 + 7y = 10$

$\sf \longmapsto7y = 10 - 10 = 0$

$\sf \bold{ y = 0}$

Now,put y's value into equation (3)

$\sf \longmapsto \: x = 5 + 2y$

$\sf \longmapsto \: x = 5 + 2(0) = 5$

$\sf \bold{x = 5}$

Check

$\sf \longmapsto \: x - 2y = 5$

$\sf \longmapsto5 - 0 = 5$

Extra information=>

Substitution method is a way of solving equations in which we substitute one variable's value from a Equation of two Variables and put into another Equation to find out the value of another Variable.