Question

How do you solve $ y = 2x + 9 $ and $ y = 9x + 10 $ using substitution?

Answer 1

Hint: Here we are given the set of equations in which the left hand side of the equations are equal and so we can substitute the values of it in one another equations resulting into one new equations with one variable and then will simplify for the resultant required value.

Complete step by step solution:
Take the given expression:
 $ \Rightarrow y = 2x + 9 $ ….. (A)
 $ \Rightarrow y = 9x + 10 $ ….. (B)
Take the equation (A)
 $ \Rightarrow y = 2x + 9 $
Now, substitute the values of “y” in the above equation from the equation (B)
 $ \Rightarrow 9x + 10 = 2x + 9 $
Now take all the constants on one side of the equation and all variables on the opposite side of the equation. Move the constant from the left hand side of the equation to the right hand side of the equation. When you move any term from one side of the equation to the opposite side then the sign of the term also changes. Negative terms become positive and vice-versa.
 $ \Rightarrow 9x - 2x = 9 - 10 $
Now, when you simplify the two like terms both having the different signs then you have to do subtraction and give a sign of a bigger term to the resultant value.
 $ \Rightarrow 7x = - 1 $
Term multiplicative on one side if moved to the opposite side, then it goes to the denominator.
 $ \Rightarrow x = - \dfrac{1}{7} $
Now, substitute the above value in the equation (A)
 $ \Rightarrow y = 2\left( { - \dfrac{1}{7}} \right) + 9 $
Simplify the above expression –
 $
 \Rightarrow y = \left( { - \dfrac{2}{7}} \right) + 9 \\
\Rightarrow y = \dfrac{{ - 2 + 63}}{7} \\
\Rightarrow y = \dfrac{{61}}{7} \\
  $

Hence, the required value is $ (x,y) = \left( { - \dfrac{1}{7},\dfrac{{61}}{7}} \right) $

Note: Be careful about the sign convention while moving any term from one side to another. While doing simplification remember the few rules. Addition of two positive terms gives the positive term, Addition of one negative and positive term, you have to do subtraction and give sign of bigger number whether positive or negative and addition of two negative numbers gives negative number but in actual you have to add both the numbers and give negative sign to the resultant answer.