Question

How do you solve \[x = 3y - 1\] and \[x + 2y = 9\] using substitution?

Answer 1

Hint: We have to solve these two equations by substitution method.
The method of solving "by substitution" works by solving one of the equations for one of the variables, and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other.
So, in the substitution method, we substitute any one of the values of \[x\] or \[y\] in the other equation.
Finally, we will get the solution.

Complete step-by-step solution:
It is given that; \[x = 3y - 1\] and \[x + 2y = 9\]
We have to solve these two equations by substitution method.
We know that, in the substitution method, we substitute any one of the values of \[x\] or \[y\] in the other equation.
Let us take,
\[x = 3y - 1\]…….... (1)
\[x + 2y = 9\]…….... (2)
We will substitute the value of \[x\] from (1) in (2).
So, we have,
$\Rightarrow$\[3y - 1 + 2y = 9\]
Simplifying we get,
$\Rightarrow$\[5y = 10\]
Simplifying again we get,
$\Rightarrow$\[y = \dfrac{{10}}{5}\]
Simplifying again we get,
$\Rightarrow$\[y = 2\]
Now, we will substitute \[y = 2\] in (1) we get,
$\Rightarrow$\[x = 3 \times 2 - 1 = 5\]
So, the values are \[x = 5\] and \[y = 2\].

Hence, the solution is \[x = 5\] and \[y = 2\].

Note: The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
In this way, a pair of the linear equations gets transformed into one linear equation with only one variable, which can then easily be solved.
The method of substitution involves three steps:
Solve one equation for one of the variables.
Substitute this expression into the other equation and solve.
Re-substitute the value into the original equation to find the corresponding variable.