# What does it mean “Solve the following system of equations by elimination: 2x + 3y = 15 and 3x + 2y = 21.”

justaguide | Certified Educator

The system of equations 2x + 3y = 15 and 3x + 2y = 21 has to be solved by elimination. Manipulate the equations and eliminate each of the variables to determine the value of the other.

2x + 3y = 15 …(1)

3x + 2y = 21 …(2)

3*(1) - 2*(2)

=> 6x + 9y - 6x - 4y = 45 - 42

=> 5y = 3

=> y = 3/5

2*(1) - 3*(2)

=> 4x + 6y - 9x - 6y = 30 - 63

=> -5x = -33

=> x = 33/5

The solution of the set of equations is x = 33/5 and y = 3/5

chaobas | Student

Elimination method means removal of one variable by comparing the equation.

the given equations are 2x + 3y = 15 and 3x + 2y = 21

let

2x + 3y = 15----------------(1)

3x + 2y = 21------------------(2)

multiplying eqn (1) by 3 and (2) by 2 we get

6x+9y=45-------->(3)

6x+4y=42-------->(4)

now subtraction eqn (4) from (3), we get

6x+9y=45

-(6x+4y=42)

------------------------------------------

9y-4y = 45-42

5y=3

y=3/5

now putting this value in eqn (1) we have

2x + 3y = 15

2x + 3*(3/5) = 15

2x+9/5 = 15

10x+9=75 [multiplying by 5]

10x=75-9 =66

x=66/10  = 33/5

so x=33/5  : y=3/5