Question

How do you solve $3x+7y=10$ and $x=18-6y$ using substitution?

Answer 1

Hint: In this question, we have to find the value of x and y. Since it is given in the question that we have to solve using the substitution method. Therefore, we start solving this problem by substituting one equation in another equation and then solve for variables. First, we substitute equation $x=18-6y$ in equation $3x+7y=10$, and make the necessary calculations to get a value of y. Then we will substitute the value of y in the equation $x=18-6y$ , to get a value of x, which is our required answer.

Complete step by step answer:
According to the question, we have to find the value of x and y.
The equation given to us is $3x+7y=10$ ---------- (1) and $x=18-6y$ --------- (2)
Therefore, we use the substitution method.
Firstly, we will substitute equation (2) in equation (1), we get
$\Rightarrow 3(18-6y)+7y=10$
Now, we will apply the distributive property $a(b-c)=ab-ac$ in the above equation, we get
$\Rightarrow 3(18)-3(6y)+7y=10$
On further simplification, we get
$\Rightarrow 54-18y+7y=10$
$\Rightarrow 54-11y=10$
Now, we will subtract 54 on both sides in the above equation, we get
$\Rightarrow 54-11y-54=10-54$
As we know, the same terms with opposite signs cancel out each other, we get
$\Rightarrow -11y=-44$
Now, we will divide 11 on both sides in the above equation, we get
$\Rightarrow -\dfrac{11}{11}y=-\dfrac{44}{11}$
Therefore, we get
$\Rightarrow -y=-4$
In the last, we will multiply (-1) on both sides in the above equation, we get
$\Rightarrow -y.(-1)=-4.(-1)$
On further simplification, we get
$\Rightarrow y=4$ --------- (3)
Now, we get the value of y, so we will substitute the value of equation (3) in equation (2), we get
$\Rightarrow x=18-6(4)$
Thus, on solving the brackets in the above equation, we get
$\Rightarrow x=18-24$
Therefore, we get
$\Rightarrow x=-6$

Therefore, for the equations $3x+7y=10$ and $x=18-6y$ , we get the value of x and y as -6 and 4 respectively.

Note: Always make all calculations properly to avoid confusion and errors. One of the alternative methods to solve this problem is you can get both equations in terms of x, and then substitute one equation into another and make the calculations, to get the value of x and y, which is our required answer.