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A Bunch of Systems

Solve each system of equations without graphing and show your reasoning. Then, check
your solutions.

2x + 3y = 7
-2x + 4y = 14

User Azul
by
3.4k points

2 Answers

2 votes

Answer:(- 1, 3 )

Explanation:

User BHP
by
4.2k points
4 votes

Answer:

(- 1, 3 )

Explanation:

2x + 3y = 7 → (1)

- 2x + 4y = 14 → (2)

add (1) and (2) term by term to eliminate x

(2x - 2x) + (3y + 4y) = (7 + 14)

0 + 7y = 21

7y = 21 ( divide both sides by 7 )

y = 3

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

substituting into (1)

2x + 3(3) = 7

2x + 9 = 7 ( subtract 9 from both sides )

2x = - 2 ( divide both sides by 2 )

x = - 1

As a check

substitute the values of x and y into the left side of both equations and if equal to the right side in both equations then the values of x and y are true.

(1) 2(- 1) + 3(3) = - 2 + 9 = 7 ← true

(2) - 2(- 1) + 4(3) = 2 + 12 = 14 ← true

then (- 1, 3 ) is the solution to the system

User Amol Gangadhare
by
4.1k points