Answer:
Option d. (6,6)
Step-by-step explanation:
(1) 4x-3y=6
(2) 6x-5y=6
Using the equal values method. Let's isolate "x" from each equation:
(1) 4x-3y=6
Adding 3y to both sides of the equation:
4x-3y+3y=6+3y
4x=6+3y
Dividing both sides of the equation by 4:
[tex]\frac{4x}{4}=\frac{6+3y}{4}\\ x=\frac{6+3y}{4}[/tex]
Isolating "x" from the second equation:
(2) 6x-5y=6
Adding 5y to both sides of the equation:
6x-5y+5y=6+5y
6x=6+5y
Dividing both sides of the equation by 6:
[tex]\frac{6x}{6}=\frac{6+5y}{6}\\ x=\frac{6+5y}{6}[/tex]
Equaling y:
y=y
[tex]\frac{6+3y}{4}=\frac{6+5y}{6}[/tex]
Solving for "y": Cross multiplication:
6(6+3y)=4(6+5y)
Applying the distributive property:
6(6)+6(3y)=4(6)+4(5y)
36+18y=24+20y
Subtracting from both sides 18y and 24:
36+18y-18y-24=24+20y-18y-24
12=2y
Dividing both sides by 2:
12/2=2y/2
6=y
y=6
Replacing y by 6 in the any of the equations where we isolated "x":
[tex]x=\frac{6+3y}{4}\\ x=\frac{6+3(6)}{4}\\ x=\frac{6+18}{4}\\ x=\frac{24}{4}\\ x=6[/tex]
The solution is (x,y)=(6,6)
Answer:
Option (d) is correct.
(6, 6) is the solution of the given system of equation.
Step-by-step explanation:
Consider the given equations
4x-3y=6 ....(1)
6x-5y=6 .........(2)
Solving system of equation using elimination method,
Multiply equation (1) by 5 , we get
(1) ⇒ 20x - 15y = 30 ......(3)
Multiply equation (2) by 3 , we get,
(2) ⇒ 18x - 15y = 18 .......(4)
Subtract equation (3) from (4) , we get,
18x - 15y -( 20x - 15y) = 18 - 30
18x - 15y - 20x +15y = -12
18x - 20x = -12
-2x = -12
⇒ x = 6
Also put x = 6 in (1) , we get
(1) ⇒ 4x - 3y = 6
⇒ 4(6) - 3y = 6
⇒ 24 - 3y = 6
⇒ - 3y = 6-24
⇒ - 3y = - 18
⇒ y = 6
Thus, Option (d) is correct.
(6, 6) is the solution of the given system of equation.
