Answer:
the solution to the system of equations is x = -1 and y = 2.
Explanation:
To eliminate the x-terms, we need to multiply one or both of the equations by a constant so that the coefficients of x in both equations become equal. In this case, multiplying Equation 1 by 3 and Equation 2 by 2 will give us the same coefficient for x:
Equation 1 (after multiplying by 3): 6x + 12y = 18
Equation 2 (after multiplying by 2): 6x + 10y = 14
Now, we can subtract Equation 2 from Equation 1 to eliminate the x-term:
(6x + 12y) - (6x + 10y) = 18 - 14
Simplifying, we get:
2y = 4
Now, we can solve for y by dividing both sides of the equation by 2:
2y/2 = 4/2
y = 2
Now that we have the value of y, we can substitute it back into either Equation 1 or Equation 2 to find the value of x. Let's use Equation 1:
2x + 4(2) = 6
Simplifying, we get:
2x + 8 = 6
Subtracting 8 from both sides, we get:
2x = -2
Dividing both sides by 2, we find:
x = -1