Solve the simultaneous equations: 12x - 4y = 12 and 3x + 2y = 12

Method 1 for solving these equations would be to multiply equation 2 (3x + 2y = 12) by 4 so that the x coefficients are equal, this becomes (12y+8x=48). Then subtract equation 1 from equation 2: (12x+8y=48) subtract (12x - 4y=12) which gives (12y=36), this equation can then by simplified by dividing 36 by the y coefficient to give y=3. This y value can then by substituted into equation 1 to find the value of x: 3x + 2(3)=12 which simplifies to 3x=6, therefore this becomes x=2. Method 2 for solving this equation involves dividing equation 1 by 4 to give (3x-y=3) which can be rearranged to give (y=3x-3) - call this equation 3. Equation 3 can then be substituted into equation 2: 3x+2(4x-3)=12, simplify this to become 9x=18, when simplified further this gives x=2. This x value can be substituted back into equation 3 to give y=3(2)-3, therefore y=3.