Question

Solve by substituting method \[3x+4y=10,\text{ }2x-2y=2\].

Answer 1

Hint:The method of solving by substitution method works by solving any one of the equation for one of the variables (here it is x and y), and then plugging this back into the other equation, substituting for the chosen variable and solving for the other. And again substitute the value and solve to get the first variable. This is how the substitution method works. As we are using a substituting method to find the values of $x$ and $y$.

Complete step by step answer:
We are given two equations as below,
\[3x + 4y = 10\] ----- (i)
\[ \Rightarrow 2x - 2y = 2\] ----- (ii)
Here, we will solve equation (ii) and put the value in equation (i) to get the final values of x and y. Solving the equation (ii), we get,
\[2x - 2y = 2\]
Taking 2 common from both the sides, we get,
\[ \Rightarrow 2(x - y) = 2(1)\]
Dividing number 2 from both the sides, we get,
\[ \Rightarrow x - y = 1\]
By transposition the above equation, we get,
\[ \Rightarrow x = 1 + y\]

Now, we will substitute the value of x in equation (i), to get the original value of x and y.
\[3x + 4y = 10\]
Substitute the value \[x = 1 + y\]in the above equation, we get,
\[ \Rightarrow 3(1 + y) + 4y = 10\]
Removing the brackets, we get,
\[ \Rightarrow 3 + 3y + 4y = 10\]
Simplify the above equation, we get,
\[ \Rightarrow 3 + 7y = 10\]
By transposition the above equation, we get,
\[ 7y = 10 - 3\]
\[ \Rightarrow 7y = 7\]

Taking numbers on one side and unknown value on the other side, we get,
\[y = \dfrac{7}{7} \\
\therefore y = 1 \\ \]
Next, substitute the value of y in the below equation, to get the value of x, we have,
\[x = 1 + y\]
Substitute \[y = 1\]in the above equation, we get,
\[ \Rightarrow x = 1 + 1\]
\[ \therefore x = 2\]

Thus, the value of x and y is \[2\] and \[1\] respectively.

Note:There are three ways to solve systems of linear equations i.e. substitution method, elimination method and graphing method. Here, we need to solve any one equation and put the value in another equation, to get the final values of x and y. In short, substitution means putting numbers in place of letters to calculate the value of an expression. Read the question carefully before solving and you can use any method to solve the equations if they have not specified which method to be used.