Solve the simultaneous equations: 3x + 2y = 9 and x + 7y = 22.

A simultaneous equations can be solved in multiple ways. You are probably familiar with substitution and elimination. Today, we will focus on substitution. As you can see, both equations represent a relation between two unknowns, x and y. To solve this problem using a substitution method we choose one of the equations. We then rearrange the equation so that one unknown is expressed purely in terms of the other unknown. The final form of our knew equation could look something like this: y = ax + b, where a and b are constants. Look at the initial two equations and think, which one would be the easiest to rearrange. Personally, I prefer the second one, since x already has a coefficient of one. So our new equation will look like this: x = -7y + 22. Now that we have x expressed in terms of y, we can substitute it to the first (still unused) equation. This will give us: 3(-7y+22) + 2y = 9. After rearranging it, we get: -19y = -57 -> y = 3. Now that we have y, we can use either of the equations to calculate x. Let's take the second equation. x + 7y = 22 with y = 3 x + 21 = 22 x = 1 We found a solution to the simultaneous equation: x = 1, y = 3. It is good to know that it does not matter which unknown or equation we start off with. If our first substitution from the first equation led to x = -2y/3 + 3, we still get the same answer. The is an exercise that you can try later :)