Question

iii) Solve: 14=3y+x; 20=2y -3x​

Answer 1

Given,

Two equations x+3y=14 and -3x+2y=20

To Find,

The value of x and y

Solution,

x+3y = 14

Multiplying the above equation with 3

3x+9y = 42

-3x+2y = 20

Adding both the equation

11y = 62

y = 62/11

Now put this value in first equation

x+3(62/11) = 14

x = 14 - 186/11

x = (154 - 186)/11

x = -32/11

Hence, the value of x is -32/11 and  y is 62/11

Answer 2

Concept

To get an equation in one variable using the elimination approach, either add or subtract the equations. When the coefficients of one variable are opposites, the equations are added to delete a variable, and when the coefficients of one variable are equal, the equations are subtracted to eliminate a variable.

Given Equations are

$3y+x=14\\2y-3x=20$

Find

We are asked to find the value of x and y.

Solution

$3y+x=14...(1) \times 3\\2y-3x=20...(2) \times 1\\9y+3x=42\\2y-3x=20$

Now add both the above equations

$11y=62\\y=\frac{62}{11}$

Now we will put the value of $y=\frac{62}{11}$ in first equation

$3y+x=14\\3(\frac{62}{11} )+x=14\\x=14-\frac{186}{11} \\x=\frac{-32}{11}$