Question

Which ordered pair below is a solution to the following system of equations? x + 2y = 7 2x − y = -1

Answer 1

Answer: (1,3)

Step-by-step explanation:

Let's solve this system of equations by elimination. We will multiply one or both equations such that when we combine the equations, one of the variables will completely cancel out.

Let's multiply the whole first equation by -2 to achieve this:

$-2(x+2y=7)$ now becomes $-2x-4y=-14$

Now let's add both equations

$-2x-4y=-14$

$2x-y=-1$

$-5y= -15$

Since we got y into a form we can solve it for, lets divide both sides by -5 to isolate it.

$\frac{-5y}{-5} = \frac{-15}{-5}$

$y=3$

Now that we have the value of y, we can substitute it into any equation to solve for x. Only if we have both x and y can we make an ordered pair. Let's use the second equation and substitute 3 for y.

$2x-3=-1$

We can now solve for x.

$2x=2$ [Adding 3 to both sides]

$x=1$ [Dividing by 2 on both sides]

We now have both x and y, so we can put it in an ordered pair to answer the question.

$(1,3)$