Question

-2x + 4y = 1 ; 3x - 6y = 9

Answer 1

-2x+4y=1
 3x-6y=9
To find x
First, change the second equation to slope equation.
Next, you will get -6y=3x+ 9 and divide everything by -6. -6y/-6 = 3x/-6 + 9/-6
Then, simplify and you will get y= -1/2x-3/2.
After that, replace the y=-1/2x-3/2 from the second equation and replace the y with (-1/2x-3/2).
Then, use the -2x from the first equation, add 4 and put one of the parentheses after 4 and put down -1/2x-3/2, put another parentheses after -1/2x-3/2, and put the equal sign (=) and after the equal sign, put 1.
Lastly, your equation will look like -2x+ 4(-1/2x-3/2) = 1. Do -2x + 4 and then, multiply the 4 with (-1/2x-3/2). The equation with look like -2x+-4/2x-12/2 = 1.
Simplify the fractions (-4/2x and 12/2) and you will get -2x and 6.
The equation will look like -2x+-2x-6=1 and then, add 6 to the left side of = and the right side of =.
Add -2x and -2x together, it will get you to -4x=-7, and divide -4 on each side.
It will look like this -4x/-4=7/-4. Your answer for x is -1 3/4 or -1.75. I'd rather go with the decimal instead of fraction.
To find y
First, use the second equation.
Next, write down 3 and replace the x with -7/4 in parentheses because I'd rather use an improper fraction instead of a decimal. After the parentheses, subtract the -6y and put =9.
Then, the equation will look like 3/1(-7/4) -6y = 9. Distribute by multiplying 3/1 and -7/4 which will get you to -21/4.
After that, multiply 4/1 to the entire equation. It will look like 4/1(-21/4 -6y = 9). The equation will look like -21 -24y= 36. Add the -21 to  both sides of the equation. You will get to -24y = 57. Divide -24y by -24 and 57 by -24. It will look like -24y/-24 = 57/-24. You will get the answer of -57/24, but you have to simplify the answer. If you divide by 3 to the numerator and denominator, you will get -19/8. However, I do prefer the decimal answer, which is -2.37.
Lastly, put the ordered pair together, since x= -1.75 and y= -2.37. Your answer will start with parentheses and then x and end with y and another parentheses, but in between x and y there's always a comma. So, your official answer is (-1.75, -2.37).