Question

How do you solve $2x+3y=6$ and $x+y=3$ using substitution?

Answer 1

Hint: Now we are given two linear equations. To solve the equations we will first use the equation $x+y=3$ to find the value of y in terms of x. now we will substitute the value of y in equation $2x+3y=6$ hence we will get a linear equation in x. solving this equation we can find the value of x. Now with help of any equation we can find the value of y by substituting the value of x. Hence we have the solution of the given equation.

Complete step by step solution:
Now we want to find the solution of the linear equation $2x+3y=6$ and $x+y=3$ .
To do so we will use the method of substitution.
Hence consider the equation $x+y=3$ .
Now in this equation we will find the value of y in terms of x. Hence we get,
$\Rightarrow y=3-x$
Now we will substitute the value of y in the equation $2x+3y=6$ . Hence we get
$\Rightarrow 2x+3\left( 3-x \right)=6$
Now we know the distributive property which says $a\left( b-c \right)=ab-ac$ hence we get,
$\Rightarrow 2x+3\left( 3 \right)-3\left( x \right)=6$
Now on simplifying the equation we get,
$\Rightarrow 2x+9-3x=6$
Now we transposing the term 9 on LHS we get,
$\Rightarrow 2x-3x=6-9$
Now on simplifying further we get,
$\Rightarrow -x=-3$
Now multiplying the whole equation by – 1 we get,
$\Rightarrow x=3$
Hence the value of x = 3.
Now substituting the value of x in the equation $y=3-x$ we get $y=0$
Hence the solution of the given equation is x = 3 and y = 0.

Note: Now note that while using substitution method we can also express x in terms of y instead of expressing y in terms of x. Also we can use any equation for substitution. Note that after we have the value of x or y always substitute this value in the other equation which has not been used.