Solve for x and y given the following two equations: 1) 3x + y = 10; 2) -4x - 2y = 2. The first step is to isolate a variable and get a solution for that variable. In equation 1, y can be isolated by adding (-3x) to both sides of the equation: -3x + 3x + y = -3x + 10, resulting in the first answer: y = -3x + 10.
This new value of y can be used in equation 2) -4x - 2(-3x + 10) = 2. Perform the multiplication to begin solving for x: -4x + 6x -20 = 2. Adding -4x + 6x = 2x results in: 2x -20 = 2. The next step is to isolate the variable. First add 20 to either side of the equation: 2x - 20 + 20 = 2 + 20. Then multiply both sides of the equation by 1/2: (1/2)2x = (1/2)22.
x = 22/2 or 11.
You can solve for y using either equation 1 or 2. In equation 2 ( -4x - 2y = 2), you substitute the value of x to get: -4(11) - 2y = 2. This yields: -44 - 2y = 2. Next add +44 to both sides to isolate the y variable: +44 - 44 - 2y = 2 + 44, resulting in -2y = 46. If you multiply both sides of this equation by (- 1/2) you get the value of y: (- 1/2) -2y = (- 1/2) 46. Therefore the value of y is -46/2 or -23.
The solution to our set of equations is x = 11, y = -23 but you should always check to make sure your answer is correct. If you plug these values into either of the original equations, the equation should work: 1) 3x + y = 10 become 3(11) -23 = 10, or 33 - 23 = 10. Now try equation 2) -4x - 2y = 2: -4(11) -2(-23) = 2, or -44 + 46 = 2. The solution is correct.