Question

How do you solve the system of equation by substitution $y=-2$ and $4x-3y=18?$

Answer 1

Hint: Solve the given equation for any one of the variables. As we have the value of $'y'$ and the given equation. But we have to find the value of $'x'$ Then we have to substitute the given value of $y$ in the given equation for that we have got the value of $'x'$ by using the substitution there are also various methods for finding the solutions.

Complete step-by-step answer:
Here we have,
The equation, $4x-3y=18$
Btu, the value of $y$ is given,
So, we have to determine the value of $'x'$
Now,
Substitute the given $y$ value into the given equation $4x-3y=18$ we get,
$\Rightarrow$ $4x-3y=18$
If $y=-2$ then,
$\Rightarrow$$4x-3\left( -2 \right)=18$
$\Rightarrow$$4x-6=18$
Take the $\left( -6 \right)$ to another side and subtract it with $18$ we get,
$\Rightarrow$$4x=18-6$
$\Rightarrow$$4x=12$
Divide $4$ with $12$ we get the value
$\Rightarrow$$x=\dfrac{12}{4}$
$\Rightarrow$$x=3$
The value of $x$ is $3.$

Hence, equation $4x-3y=18$ is solved by substitution and the solution to the system of equation is $x=3$ and $y=-2$.

Additional Information:
The method of solving by substitution works by solving one of the equations for one of the variables. [variable you choose is in your hand] and then adding this back
Into another equation” substituting for the chosen variable and solving for others. Then again solve it for the first variable. The problem we solve in the given question has given you the idea to solve one of the equations for one of the variables, and plug this into another question. It does not matter which equation or variable you choose. There is no right or wrong choice, the answer you get will be the same.

Note:
When you are solving the problem check the given values. Then you get the idea of what we have to find. Firstly you have to simplify the given equation by expanding. After that check the step whether you have solved for the correct variable as not also substitute the proper value which is given. Finally after getting all the values analyse the problem totally. Check all the possibilities where problems get wrong. Recalculate the values sometime it gets incorrect. These are some key points which you have to remember.