Question

use the elimantion method to solve the system of equations . choose the correct ordered pair . 7x+3y=30 -2x+3y=3

Answer 1

Explanation:

7x+3y=30

-2x+3y=3

Solving by elimination is a process by which one of the variables is eliminated by rearranging one equation and using it in the other.

We can take either equation and isolate one of the unknowns, x or y.

Lets try isolating y from the second equation:

-2x+3y=3

3y= 2x + 3

y= (2x + 3)/3 or (2/3)x + 1

y = (2/3)x + 1

Now use this definition of y in the first equation.

7x+3y=30

7x+3((2/3)x + 1) = 30 using y = (2/3)x + 1

7x+2x + 3 = 30

9x = 27

x = 3

Now use x = 3 in either equation to find y:

3y= 2x + 3

3y= 2*(3) + 3 for x = 3

3y = 9

y = 3

The solution is (3,3), which is the point the two lines intersect. See the attached graph.

Answer 2

(3, 3 )

Explanation:

given the system of equations

7x + 3y = 30 → (1)

- 2x + 3y = 3 → (2)

subtract (2) from (1) term by term to eliminate y

(7x - (- 2x)) + (3y - 3y) = 30 - 3

7x + 2x + 0 = 27

9x = 27 ( divide both sides by 9 )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (1)

7(3) + 3y = 30

21 + 3y = 30 ( subtract 21 from both sides )

3y = 9 ( divide both sides by 3 )

y = 3

the solution is (3, 3 )