In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0, b ≠ 0 5ax + 4y = 17ax + 7y = 22

A system of equations consists of two or more equations with the same variables. The goal is to find values for the variables that satisfy all equations simultaneously. In this case, we have two linear equations in terms of x and y, which can be solved using methods such as substitution or elimination.

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation. This allows us to express one variable in terms of the other, making it easier to find the values of x and y. This method is particularly useful when one equation is already solved for a variable.

The elimination method involves adding or subtracting equations to eliminate one of the variables, allowing for the other variable to be solved directly. This method is effective when the coefficients of one variable can be made equal, facilitating the cancellation of that variable when the equations are combined.