Solve the simultaneous equations: 3a + 2b = 17 and 4a - b = 30

Here we have a pair of simultaneous equations with two unknowns. There are two methods of going about this question: substitution or elimination. Today, we shall be focusing on the latter. We need a pair of common coefficients to be able to solve this for any one of the unknowns. For example 5b in the first as well as the second equation. To achieve this, we can multiply the second equation by two. This will give us 8a - 2b = 60. Both the equations now have a common term of 2b. We can ignore the signs here. The next step is to eliminate this common term. If we add the two equations together, this is possible as +2b + -2b cancels out. Therefore, we are left with 11a = 77, which can be solved like a linear equation. If both sides are divided by 11, we find that a=7. We have now found one of the two unknowns. Its very simple to find the out what b is now. We can substitute our known value of a into any one of the equations. If we put a=7 into the first, we get (3x7) + 2b = 17, therefore, 21 + 2b = 17. Once again, a linear equation can be solved. 2b = -4 and so b= -2.