solve by eliminating method 3x_4y=20;x+2y=5
Answers
Answer:
The solution of the given simultaneous equations is ( x, y ) = ( 6, - 0.5 ).
Step-by-step-explanation:
The given simultaneous equations are
3x - 4y = 20 &
x + 2y = 5.
3x - 4y = 20 - - ( 1 )
x + 2y = 5 - - ( 2 )
By multiplying equation ( 2 ) by 2, we get,
2 ( x + 2y ) = 5 × 2
→ 2x + 4y = 10 - - ( 3 )
By adding equation ( 1 ) & equation ( 3 ), we get,
→ 3x - 4y + 2x + 4y = 20 + 10
→ 5x + 0 = 30
→ 5x = 30
→ x = 30 ÷ 5
→ x = 6
By substituting x = 6 in equation ( 2 ), we get,
x + 2y = 5 - - ( 2 )
→ 6 + 2y = 5
→ 2y = 5 - 6
→ 2y = - 1
→ y = - 1 ÷ 2
→ y = - 0.5
∴ The solution of the given simultaneous equations is ( x, y ) = ( 6, - 0.5 ).
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Additional Information:
1. Linear Equations in two variables:
The equation with the highest index (degree) 1 is called as linear equation. If the equation has two different variables, it is called as 'linear equation in two variables'.
The general formula of linear equation in two variables is
ax + by + c = 0
Where, a, b, c are real numbers and
a ≠ 0, b ≠ 0.
2. Solution of a Linear Equation:
The value of the given variable in the given linear equation is called the solution of the linear equation.
3. Elimination method to solve linear equations:
1. Elimination means to remove / delete something.
2. In this method, we have to equate the coefficients of any one of the two variables in one equation.
3. And to eliminate it, we have to perform opposite operations as per the sign of the coefficient.
4. If one coefficient is positive ( + ) & another is negative ( - ), add both equations.
5. If the coefficients of both the equations have same signs ( + or - ), subtract them.
GIVEN:
3x-4y=20
................ {Given Equations}
x+2y=5
TO FIND:
Value of x and y =?
SOLUTION: (Elimination Method)
3x-4y=20....................(1)
x+2y=5........................ (2)
Multiplying equation (2) by 2 we get,
2x+4y=10..................(3)
Adding equations (1) and (3) we get,
5x=30
x=30/5
x=6
Substituting the value of x in (2) we get,
x+2y=5........ (2)
6+2y=5......
2y=5-6
2y=-1
y= -1/2
Therefore, (6, -1/2) is the solution of given simulations equation.
Substitution Method:
3x-4y=20.................(1)
x+2y=5......... (2)
From equation (2),..
x+2y=5
x=5-2y
Substituting the value of x in (1) we get,
3(5-2y) -4y=20............ (1)
15-6y-4y=20
15-10y=20
-10y=20-15
-10y=5
-y=5/10
-y=1/2
y= -1/2
Substituting the value of y in equation (2),
x+2y=5.......... (2)
x+2(-1/2) =5
x-2/2=5
x-1=5
x=5+1
x=6
Therefore, (6, -1/2) is the solution of given simultaneous equations.
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