Question

Solve the system using elimination. Write the solution as an ordered pair. (1 point) SHOW YOUR WORK FOR FULL CREDIT! (2 points)

13x + y = 15
-9x - 3y = -15

Answer 1

The solution of the system of equation is (1 , 2)

Explanation:

The system of equation is:

* 13x + y = 15 ⇒ (1)

* -9x - 3y = -15 ⇒ (2)

- By using elimination ⇒ we must make on of the

two variables in the two equations has the same value

with different sign

- So we will multiply equation (1) by 3 to eliminate y

∴ 3(13x) + 3(y) = 3(15)

∴ 39x + 3y = 45 ⇒ (3)

- Now add (2) and (3)

∴ 39x + -9x = 45 + -15

∴ 30x = 30 ⇒ ÷ 30 both sides

∴ x = 1

- Substitute the value of x in equation (1) or (2)

- Lets use (1)

∴ 13(1) + y = 15

∴ 13 + y = 15 ⇒ subtract 13 from both sides

∴ y = 15 - 13

∴ y = 2

∴ The solution of the system of equation is (1 , 2)

Answer 2

Answer: (1,2)

Explanation:

You must:

- Multiply the first equation by 3.

- Add both equations.

- Solve for the variable left. In this case will be x.

Then:

`\left \{ {{39x +3y = 45} \atop {-9x - 3y = -15}} \right.\\------\\ 30x=30\\x=1`

Substitute x=1 into any of the original equtions and solve for y:

`13(1)+y=15\\y=2`

The solution is: (1,2)