Solve the following system using the elimination method:
-3x + 4y = 6
9x - 12y = -18
By using elimination method, one of the variables must be eliminated by adding the two equations.
-3x + 4y = 6
9x - 12y = -18
We first choose the variable we want to eliminate. In here, let's choose x. To eliminate x, the term with variable x must have the same numerical coefficient (number before the variable) but have different signs (so that they would cancel). Thus, we multiply the first equation by 3:
3*(-3x + 4y) = 3*6
-9x + 12y = 18
Then we add the two equations:
-9x + 12y = 18
9x - 12y = -18
---------------------
0 + 0 = 0
Note that when you come up with this situation, this only means that the two lines are coinciding, meaning the solution is INFINITE. If however, the value of the constant (right side of equation) is not equal to zero, the lines are parallel and there is no solution.
Hope this helps~ :)
To solve the given system of equations using the elimination method, we need to manipulate the equations to get the same coefficient for either x or y in both equations.
Let's start by multiplying the first equation by 3 to make the coefficient of x in both equations equal:
(3)(-3x + 4y) = (3)(6)
-9x + 12y = 18
Now we need to subtract the second equation from this modified first equation:
(-9x + 12y) - (9x - 12y) = 18 - (-18)
-9x + 12y - 9x + 12y = 18 + 18
0 + 24y = 36
24y = 36
y = 36 / 24
y = 3/2
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
-3x + 4(3/2) = 6
-3x + 6 = 6
-3x = 6 - 6
-3x = 0
x = 0
Therefore, the solution to the system of equations is x = 0 and y = 3/2.
To solve the system using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations.
Step 1: Multiply both sides of the first equation by 3 to make the coefficient of x the same as the coefficient of x in the second equation:
(-3x + 4y) * 3 = 6 * 3
-9x + 12y = 18
Step 2: Now we can add the two equations together to eliminate x:
(-9x + 12y) + (9x - 12y) = 18 + (-18)
0 + 0 = 0
The result is 0 = 0, which means that the two equations are equivalent. This indicates that the system of equations has infinitely many solutions. The two equations represent the same line and intersect at every point on that line.
Therefore, the solution to the system is any point that satisfies both equations.