Solve the simultaneous equations: 2x - y = 4 and x + 2y = 7

Solve: 2x - y = 4  and x + 2y = 7

There are two methods to solve this, you can either calculate one of the variables from either equations and then substitute to the second one or try to multiply one of the equations so that you can add equations and eliminate one variable. This time I will use second method because it will be faster. So you need to focus on which equation would be easier to multiply by what integer so that one of the variables will have same coefficients. I suggest multiplying first equation by 2. We get then 4x-2y=8 and x +2y=7. Remember to multiply all parts of the equation, including terms on the right side that don't contain variables. Now we can add equations: 4x - 2y +x + 2y = 8 + 7 => 5x = 15 => x =3.

Now we can substitute x to equation two, rearrange it and calculate y => 3 +2y=7 => 2y=7-3 => 2y =4 => y =2.

The solution for simultaneous equation is hence x = 3 and y = 2.