Question

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Solve the following system of equations algebraically using the ELIMINATION METHOD. Show all work.
x-3y=1
3x-5y=11

Answer 1

Answer: x = 7 y = 2

(7, 2)

Explanation:

Multiply the first equation by -3 and the second by 1:

-3(x - 3y = 1)

1(3x - 5y = 11)

Becomes:

-3x + 9y = -3

3x - 5y = 11

Add the equations to eliminate x:

-3x + 9y = -3

3x - 5y = 11

4y = 8

Solve for y by dividing by 4:

4y/4 = 8/4

y = 2

Now we plug in y to the first equation:

x - 3 ( 2 ) = 1

x - 6 = 1

Add 6 to both sides:

x - 6 + 6 = 1 + 6

x = 7

Answer 2

(7,2)

Explanation:

Multiply the first equation by -3

(x-3y=1) = -3x+9y=-3

Combine like terms with the new equation and the second equation

(-3x+9y=-3) + (3x-5y=11) = 4y=8

Divide each side by 4

4y/4=8/4

y=2

Plug in 2 for y in any equation. It doesn’t matter which one

x-3(2)=1

Distribute

x-6=1

Add 6 to both sides

x-6=1

+6 +6

x=7