Question

Directions: Use substitution to solve the systems of equations.
y = 2x
x - y = 1

Answer 1

To use substitution, you substitute one of the equations into the other for one of the variables.

Since the first equation is already solved for y, let's substitute that one into the second equation.

Before substitution: x - y = 1

After substitution:    x - 2x = 1

See how we replaced the y with 2x? This is because the first equation is y = 2x.

Combine like terms.

-x = 1

Multiply each side by -1 so we get the value of x, not -x.

x = -1

We can now solve for y using the 1st equation, substituting the value for x into it.

Before: y = 2x

After:    y = 2(-1)

Multiply the two together.

y = -2

Let's check this in the second equation, so we know we didn't make a mistake somewhere.

Before: x - y = 1

After:   (-1) - (-2) = 1

Subtracting a negative is the same as adding a positive, so let's notate it that way to make it easier.

-1 + 2 = 1

Add.

1 = 1

Since both sides are equal, that means we've got the correct solution.

The notation for our answer will be (x, y) since it is a point on a graph.

Your final answer is (-1, -2).

Answer 2

substitute y=2x in x-y=1

x-2x=1

-x=1

x=-1

and y=2x

so, y=-2

x=-1,y=-2