6x – 4y=-12; 8x – 3y = -2 then solution of given equation are O (2-1) O (4,-1) O (2,6) O (1,-1)
The Correct Answer and Explanation is:
To find the solution to the given system of equations:
1) 6x – 4y = -12
2) 8x – 3y = -2
Use the method of elimination or substitution. Begin by eliminating one variable.
Step 1: Eliminate one variable
To eliminate y, multiply both equations so that the y terms have a common coefficient:
Multiply equation (1) by 3:
3(6x – 4y) = 3(-12) → 18x – 12y = -36
Multiply equation (2) by 4:
4(8x – 3y) = 4(-2) → 32x – 12y = -8
Now subtract the first new equation from the second:
(32x – 12y) – (18x – 12y) = -8 – (-36)
(32x – 18x) = 28
14x = 28
x = 2
Step 2: Substitute back to find y
Use x = 2 in one of the original equations, say equation (1):
6x – 4y = -12
6(2) – 4y = -12
12 – 4y = -12
-4y = -24
y = 6
Solution: x = 2, y = 6 → (2, 6)
Now check the options:
- (2, -1) → incorrect
- (4, -1) → incorrect
- (2, 6) → ✅ correct
- (1, -1) → incorrect
Explanation
Solving a system of linear equations involves finding values for the variables that satisfy both equations simultaneously. In this case, two linear equations are given with variables x and y. One effective method for solving such systems is the elimination method. This method aims to eliminate one variable so the other can be solved directly.
First, both equations are manipulated to create matching coefficients for the y variable. By multiplying the first equation by 3 and the second by 4, both yield terms involving -12y. Subtracting these new equations eliminates y, resulting in a simplified equation involving only x. This step reveals the value of x as 2.
With x known, substitution back into either original equation gives the corresponding value for y. Plugging x = 2 into the first equation allows solving for y easily, yielding y = 6.
Finally, the point (2, 6) satisfies both original equations, confirming it as the correct solution. Among the answer choices provided, only the option (2, 6) matches this solution. The process demonstrates the utility of the elimination method for solving linear systems and confirms that careful arithmetic ensures accurate results.
