Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-3x + 6y = -3 / -6x + 4y = -10
Eq1: -3X + 6Y = -3
Eq2: -6X + 4Y = -10
Multiply Eq1 by -2 and add the Eqs:
6X - 12Y = 6
-6X + 4Y = -10
Sum: -8Y = -4.
Y = 1/2.
Substitute 1/2 for Y IN Eq1
-3X + 3 = -3,
-3X = -6,
X = 2.
Solution Set = (2, 1/2).
To solve the system of equations using the elimination method, we'll manipulate the equations in order to eliminate one of the variables. Here's how to do it step by step:
1. Multiply both sides of the first equation by 2 to make the coefficient of y the same in both equations:
-3x + 6y = -3 ---> -6x + 12y = -6
2. Multiply both sides of the second equation by 3 to make the coefficient of y the same in both equations:
-6x + 4y = -10 ---> -18x + 12y = -30
Now, we have two equations with the same coefficient for y:
-6x + 12y = -6
-18x + 12y = -30
3. Now, let's subtract the first equation from the second equation, which will eliminate y:
(-18x + 12y) - (-6x + 12y) = -30 - (-6)
-18x + 12y + 6x - 12y = -30 + 6
-18x + 6x = -24
-12x = -24
4. Divide both sides of the equation by -12:
(-12x) / (-12) = (-24) / (-12)
x = 2
Now that we found the value of x, we can substitute it into one of the original equations to find the value of y.
Let's substitute x = 2 into the first equation:
-3x + 6y = -3
-3(2) + 6y = -3
-6 + 6y = -3
5. Add 6 to both sides of the equation:
-6 + 6y + 6 = -3 + 6
6y = 3
6. Divide both sides of the equation by 6:
(6y) / 6 = 3 / 6
y = 1/2
Therefore, the solution to the system is x = 2 and y = 1/2.