Question

How do you solve $x=y+3$ and $2x+y=9$ ?

Answer 1

In this question, we have to find the value of x and y. In this question, there are two equations for solving this problem, we use the substitution method. We find the value of x in respect of y from equation 1 and substitute that value in equation 2. Then, apply distributive property $a(b+c)=ab+ac$and subtract 6 on both sides of the equation. Again, divide both sides by 3 to get the value of y. Now, substitute the value of y in the equation of x to get the required answer.

Complete step by step answer:
According to the question, it is given that there are two equations, that is
$f({{x}_{1}}):x=y+3$ -------- (1)
$f({{x}_{2}}):2x+y=9$ ------- (2)
Let us find the value of x with respect to y from equation (1), we get
$x=y+3$ --------- (3)
Now, we substitute the value from equation (3) to equation (2), therefore, we get
$\begin{aligned} & 2x+y=9 \\\ & \Rightarrow 2(y+3)+y=9 \\\ \end{aligned}$
Now, apply distributive property $a(b+c)=ab+ac$ in the LHS of the above equation, we get
$\Rightarrow 2(y)+2(3)+y=9$
On further solving the above equation, we get
$\begin{aligned} & \Rightarrow 2y+6+y=9 \\\ & \Rightarrow 3y+6=9 \\\ \end{aligned}$
Now, subtract 6 on both sides of the equation, we get
$\Rightarrow 3y+6-6=9-6$
As we know, the same terms will cancel with the different signs, we get
$\Rightarrow 3y=3$
Now, divide both sides by 3 in the above equation, we get
$\begin{aligned} & \Rightarrow \dfrac{3}{3}y=\dfrac{3}{3} \\\ & \Rightarrow y=1 \\\ \end{aligned}$
Now, we get the value of y=1. Again substitute the value of y=1 in equation (3), we get
$\begin{aligned} & x=y+3 \\\ & \Rightarrow x=1+3 \\\ & \Rightarrow x=4 \\\ \end{aligned}$
Thus, we get the value of x=4.
Therefore for the equations $x=y+3$ and $2x+y=9$ , we get the required answer as x=4 and y=1.

Note: For checking your answer put the value x and y in both the equations, if you get the answer as 0, your answer is correct. Otherwise, you have made a mistake somewhere in the solution. One of the alternative methods for finding the value of x and y is the elimination method. In this method, add both the equations to get a single equation, which gives you the value x and y.