Question

How do you solve the equation $2x+2y=14$ and $2x-y=5$ using substitution.

Answer 1

Hint: Now we have two equations in x and y. to solve the equations we will first use the equation $2x-y=5$ to write y in terms of x. Now we will substitute the value of y with the other equation and hence we will get the value of x. Now substituting the value of y in any equation and simplifying we get the value of x.

Complete step by step solution:
Now we are given with two linear equations in x and y.
We will solve the two linear equations using a method of substitution.
Hence first let us consider the equation $2x-y=5$ .
Now we will use the equation to find the value of y in terms of x.
Now rearranging the terms of the equation by taking y on RHS and 5 on LHS we get,
$\Rightarrow y=2x-5$
Now consider the equation $2x+2y=14$
We can see that we can simplify the equation by dividing the equation by 2.
Hence we get $x+y=7$
Now substituting the value of y in the above equation we get,
$\Rightarrow x+\left( 2x-5 \right)=7$
Now separating constant terms and variables we get,
$\Rightarrow 2x+x=7+5$
Hence on simplifying the equation we have $3x=12$
Now dividing the whole equation by 3 we get, x = 4
Hence the value of x is 4. Now substituting the value of x in $y=2x-5$ we get
$\begin{align}
  & \Rightarrow y=2\left( 4 \right)-5 \\
 & \Rightarrow y=8-5 \\
 & \Rightarrow y=3 \\
\end{align}$

Hence the solution of the given equation is x = 4 and y = 3.

Note: Now note that we can also solve this equation by eliminating the variables in the equation. To do so, multiplying both equations with an appropriate number such that we get the coefficient of one variable will be the same. Now we will add or subtract the two equations such that the terms will get subtracted and we get a linear equation in one variable.