Question

Solve $3x+4y=10$ and $2x-2y=2$ by substitution method.

Answer 1

Hint: By using method of substitution try to convert the variable y in terms of x from any equation. Now substitute the value of y back into the remaining equation. By this you get a relation in y. Try to bring all y terms on the left side, after this the value on right side will be the value of y. By using this y value, get a value of x. The pair of values will be your result. Now verify them by substituting in any one of them.

Complete step-by-step solution -
Substitution Method: The method of solving a system of equations. It works by solving one of the equations for one of the variables to get in terms of another variable, then plugging this back into another equation, and solving for the other variable. By this you can find both the variables. The method is generally used when there are 2 variables. For more variables it will be tough to solve.
Given expression which we need to solve are given by:
$3x+4y=10$ …………………..(i) $2x-2y=2$ ………………………………..(ii)
By dividing with 2 on both sides of equation (ii), we get
$\Rightarrow x-y=1$
By adding y on both sides of above equation, we get:
$\Rightarrow x-y+y=y+1$
By cancelling the common terms on left hand side, we get:
$\Rightarrow x=y+1$ …………………………(iii)
By substituting equation (iii) in equation (i), we get the equation:
$\Rightarrow 3\left( y+1 \right)+4y=10$
To remove parenthesis, we must multiply 3 inside the bracket:
$\Rightarrow 3y+3+4y=10$
By subtracting 3 on both sides of above equation, we get
$\Rightarrow 3y+4y=7$
By taking y common on left hand side, we get:
$\Rightarrow y\left( 3+4 \right)=7$
By dividing with 7 on both sides of the equation, we get:
$\Rightarrow \dfrac{7y}{7}=\dfrac{7}{7}$
By simplifying above equation, we get the value of y to be:
$\Rightarrow y=1$
By substituting this value into equation (iii), we get x as:
$\Rightarrow x=1+1=2$
For verification, we substitute x, y into equation (ii).
By substituting $x=2,y=1$ in equation (ii), we get:
$2\left( 2 \right)-2\left( 1 \right)=2$
By simplifying left hand side of above equation, we get:
$2=2$
So, this is true. Hence, Verified.
Therefore, the solution of given equations as $\left[ 2,1 \right]$ .

Note: Be careful while removing brackets. Don’t forget that the constant must also be multiplied. Generally, students multiply variables and forget about constant. Verification of a solution must be done to prove that our result is correct. Similarly, you can first find x in terms of y and then substitute and continue. Anyways, you will get the same result because the values of x, y won’t change.