Question

Solve using substitution:

4x- 2y = 6 and x + y = 6


solve using elimination:

4x- 2y = 6 and x + y = 6

Answer 1

Explanation:

Substitution is a method that rewrites one of the equations in terms of one variable, and substitutes that in the other equations.

We can easily rewrite x + y = 6 by subtracting y from both sides, giving us

`x = -y+6`

By putting this equation in place of x in the first equation, we can solve for y:

`4(-y+6)-2y=6`

`-4y+24-2y=6` [Distributing 4 into the parentheses]

`-6y+24=6` [Combining like terms]

`-6y = -18` [Subtracting 24 from both sides]

`y=3` [Dividing both sides by -6]

Since we solved for y, we can again substitute by putting it into the second equation.

`x+3=6`

`x=3` [Subtracting 3 from both sides]

The solution for this system of equations is (3,3).

Elimination is another method of solving systems of equations. In this method, we multiply one equation such that when both equations are combined, only one variable is left.

We can first multiply both sides of the second equation by 2.

`2x+2y=12`

Now, let's add both equations to cancel out y.

`4x-2y=6`

`2x+2y=12`

`6x=18`

Now, we can divide 6 from both sides to get the value of x.

`(6x)/(6) = (18)/(6)`

`x=3`

We can now substitute this value into one of the equations to get the value of y. Here, I used the second equation.

`3+y=6`

`y=3`

The solution to our system of equations is (3,3).