211k views
5 votes
5.- 6x + y = 66x + 3y =- 12

User Ccampo
by
3.8k points

1 Answer

2 votes
System of equations

We are going to use the Elimination Method.

This is: we are going to add both sides of the equations so our result is an equation with just one variable.

Step 1

We have that if we add the equations, we will eliminate the x term, then we go ahead:

- 6x + y = 6

6x + 3y =- 12

____________

0x + 4y = -6

because -6x + 6x = 0x, y + 3y = 4y and 6 - 12 = -6

Step 2

Now, we have an equation for y

0x + 4y = -6

4y = -6

Taking 4 to the right side of the equation:

4y = -6

y = -6/4 = -1.5

Then y = -1.5

Step 3

Now we find x by replacing y = -1.5 in any of the given equations:

-6x + y = 6

-6x - 1.5 = 6

Taking -1.5 and -6 to the right side of the equation:

-6x - 1.5 = 6

↓ taking -1.5

-6x = 6 + 1.5 = 7.5

-6x = 7.5

↓ taking -6

x = 7.5/(-6) = -1.25

Then x = -1.25

Answer- the solution of the system is x = -1.25 and y = -1.5: (-1.25, -1.5)

User Theodore Lytras
by
4.2k points