Example Question - solving for variables

Solving a System of Equations by Addition Method

The system of equations provided is: -5x - 6y = -2 4x + 6y = -2 This system can be solved by adding the two equations together, as the y terms will cancel each other out given they have opposite coefficients. Adding the left sides of the equations: -5x - 6y + 4x + 6y = -2 + (-2) Combining like terms: -5x + 4x = -x -6y + 6y = 0 -2 - 2 = -4 So we have: -x = -4 Dividing both sides by -1 to solve for x: x = 4 Now that we have a value for x, we can substitute this value into either one of the original equations to find the value of y. Let's use the first equation: -5x - 6y = -2 Substitute x = 4: -5(4) - 6y = -2 -20 - 6y = -2 Add 20 to both sides to isolate terms with y: -6y = -2 + 20 -6y = 18 Divide both sides by -6 to solve for y: y = 18 / -6 y = -3 The solution to the system of equations is: x = 4 y = -3