4x+3y=4:6x+5y=8 solutions please by equating coefficients
Answers
Answer:
x=-2, y=4
Step-by-step explanation:
hope this helps you
Answer:
The solution of the given simultaneous equations is ( x, y ) = ( - 2, 4 ).
Step-by-step-explanation:
The given simultaneous equations are 4x + 3y = 4 and 6x + 5y = 8.
4x + 3y = 4 - - ( 1 )
6x + 5y = 8 - - ( 2 )
By multiplying equation ( 1 ) by 5 and equation ( 2 ) by 3, we get,
20x + 15y = 20 - - ( 3 )
18x + 15y = 24 - - ( 4 )
Now, by subtracting equation ( 3 ) from equation ( 4 ), wet,
18x + 15y = 24 - - ( 4 )
-
20x + 15y = 20 - - ( 3 )
(-)........(-)...... (-)
_______________
⇒ - 2x = 4
⇒ x = - 4 / 2
⇒ x = - 2
By substituting x = - 2 in equation ( 1 ), we get,
4x + 3y = 4
⇒ 4 × ( - 2 ) + 3y = 4
⇒ - 8 + 3y = 4
⇒ 3y = 4 + 8
⇒ 3y = 12
⇒ y = 12 ÷ 3
⇒ y = 4
∴ The solution of the given simultaneous equations is ( x, y ) = ( - 2, 4 ).
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.