Which is a solution what system of equations 2X-y equals 6 and X-3y equals 8?

Answer 1

Method 1: Solving by Elimination

This can be done with either x or y. Either x or y is made equal in each equation and then subtracted. The set of equations looks like:

2x-y=6

x-3y=8

Step 1: X can be made equal if the bottom equation is multiplied by 2. The set of equations now looks like:

2x-y=6

2x-6y=16

Step 2: Subtract the second equation from the first and solve.

5y=-10

y=-2

Step 3: Now substitute -2 for y in either equation to solve x.

x-3y=8

x-3(-2)=8

x+6=8

x=2

The solution is (2, -2).

Method 2: Solving by Substitution

Solve for y in one of the equations, then substitute it into the other for x. This can be done with either x or y and in either equation.

Step 1: Solve for y in one equation

2x-y=6

2x=6+y

2x-6=y

y=2x-6

Step 2: Substitute y into the other equation and solve for x

x-3y=8

x-3(2x-6)=8

x-6x+18=8

-5x+18=8

-5x=-10

x=2

Step 3: Substitute x into the first equation

y=2x-6

y=2(2)-6

y=4-6

y=-2

The solution is (2,-2)