Solve algebraically: 6a+b=16, 5a-2b=19

To solve these simultaneous equations, you must add/subtract both equatons from each other to eliminate one variable, allowing you to work out the value of the other.

As you can see from these particular equations, you must manipulate one to eliminate the variable. In this case you can multiply the first equation by 2 to give 12a+2b=32. Now you can add this new equation to the second equation (5a-2b=19) to give 17a=51. Since the 'b' variable has been eliminated, you can now find the value of a, which is 51/17=3.

Substitute this value of a into any of the equations given in the question to find b. Substituting into the first, we have (6*3)+b=16. This gives b=4, so the answers are a=3, b=-2