Solve the simultaneous equations 2x + 3y = 6 - 3x and 5x + 6y = 10 - y.

Step 1: First it is best to rearrange the to simultaneous equations to have the unknown variables on one side and the constants on the other: 5x + 3y = 6 and 5x + 7y = 10.Step 2: Next is to notice that both equations share '5x' as a term which allows it to be cancelled out by taking one equation away from the other. We shall take away the equation with smaller y coeffecient from the equation with larger y coeffecient:(5x + 7y) - (5x + 3y) = 4y and 10 - 6 = 4 which gives us: 4y = 4 and such y=1.Step 3: Finally we must solve for x by substituting the value of y=1 into one of the equations:5x + 3 = 6 so 5x = 3. Dividing by 5 gives us x = 3/5 and y=1. (Another step can be added here by substituting both the x and y into the other equation as a form of self-checking: 3 + 7 = 10 which is true.)