) 6x+2y=12 2x+2y=8 4x+12y=2 4

To solve the system of equations, we can use the method of substitution or elimination. Let's use the elimination method.<br /><br />First, we can eliminate the variable y by multiplying the second equation by -2 and adding it to the first equation:<br /><br />-2(2x + 2y) + (6x + 2y) = -2(8) + 12<br />-4x - 4y + 6x + 2y = -16 + 12<br />2x - 2y = -4<br /><br />Now, we can eliminate the variable y by multiplying the third equation by -1/12 and adding it to the first equation:<br /><br />-1/12(4x + 12y) + (6x + 2y) = -1/12(2) + 12<br />-1/3x - y + 6x + 2y = -1/6 + 12<br />5/3x + y = 12 - 1/6<br />5/3x + y = 71/6<br /><br />Now we have two new equations:<br />2x - 2y = -4<br />5/3x + y = 71/6<br /><br />We can solve this system of equations by multiplying the second equation by 2 and adding it to the first equation:<br /><br />2(5/3x + y) + (2x - 2y) = 2(71/6) + (-4)<br />10/3x + 2y + 2x - 2y = 71/3 - 4<br />14/3x = 65/3<br />x = 65/14<br /><br />Now we can substitute the value of x into the second equation to find the value of y:<br />5/3(65/14) + y = 71/6<br />y = 71/6 - 5/3(65/14)<br />y = 71/6 - 25/6<br />y = 46/6<br />y = 23/3<br /><br />Therefore, the solution to the system of equations is x = 65/14 and y = 23/3.