Question

Identify a possible first step using the elimination method to solve the system and then find the solution to the system. 2x − 5y = 11 3x + 2y = 7

Answer 1

In order to use the elimination method, we have to multiply the equation by some number, so that one of the variable has the same coefficient.

For example, multiplying the first equation by 3 and the second by 2 gives the following, equivalent system:

`\begin{cases}6x-15y=33\\6x+4y=14\end{cases}`

Now, we can subtract the two equations, and we will cancel (eliminate) the x variable:

`-19y=19 \iff y=-1`

Now that y is known, plug it into one of the equations: for example, if we use the first one we get

`2x+5 = 11 \iff 2x = 6 \iff x=3`

Answer 2

Multiply first equation by −3 and second equation by 2, solution (3, −1).

Explanation: