Solve the simultaneous equations: 8x + 2y =46, and 7x + 3y = 47

Whenever we have two equations with two unknowns (x and y) to solve simultaneously, we can try to substitute one equation into the other. If we were to multiply every term in equation 1 by 1.5, then we would have a 3y term in each equation. Equation 1 becomes 12x + 3y = 69, and equation 2 is still 7x + 3y = 47. If we rearrange for the 3y term in equation 1, we get 3y = 69 - 12x. We can now substitute this value for 3y into equation 2. This give us a new equation, let's call it equation 3, which is of the form 7x + 69 - 12x = 47. Now we collect like terms to simplify the equation. Doing this gives us -5x = -22. Multiplying both sides by -1 gives us 5x = 22. Dividing through by 5 gives tells us that x = 22/5.

Now let's substitute this value for x back into equation 1. We now have 8*(22/5) + 2y = 46. We can times out the bracket to get 176/5 + 2y = 46. Collecting like terms gives us 2y = 54/5. Dividing by 2 gives us y = 27/5.