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Slav-nsk [51]
3 years ago
13

2x - y = 5 5x + y = 16

Mathematics
2 answers:
Paha777 [63]3 years ago
8 0

Answer:

(3, 1)

Step-by-step explanation:

To find the solution (point of intersection) of a system of linear equations, first convert them to <u>slope-intercept form</u> (y=mx+b) by isolating "y". Then, equate their expressions to find "x". Substitute what you find for "x" to find the coordinate for "y".

<u>Isolate "y" in each equation</u>

2x - y = 5     Subtract 2x from both sides

-y = -2x + 5     Divide the whole equation by -1 to isolate "y"

-y/(-1) = -2x/(-1) + 5/(-1)     Each term's negative/positive sign changes

y = 2x - 5

5x + y = 16     Subtract 5x from both sides

5x - 5x + y = -5x + 16     The 5x on left cancel out (5x - 5x = 0)

y = -5x + 16

Since y = 2x - 5 and y = -5x + 16 both equal y, we can make them equal each other. Then isolate "x" to be on the left side.

<u>Equate the equations</u>

y = y

2x - 5 = -5x + 16

2x - 5 + 5x = -5x + 5x + 16     Add 5x to both sides

2x - 5 + 5x = 16     Right side 5x cancelled out (-5x + 5x = 0)

7x - 5 = 16     Combined like terms on left (2x + 5x = 7x)

7x - 5 + 5 = 16 + 5     Add 5 to both sides.

7x = 16 + 5     Left side cancelled out (-5 + 5 = 0)

7x = 21     Simplified right side.

7x/7 = 21/7     Divide both sides by 7

x = 21/7     Since 7/7=1, 7x/7 = x , and "x" is isolated.

x = 3     Found "x" coordinate of solution.

<u>Substitute x = 3</u> into any equation

2x - y = 5

2(3) - y = 5        Simplify first by multiplying 2 and 3 on left side

6 - y = 5        Start isolating "x"

6 - y + y = 5 + y        Add "y" to both sides.

6 = 5 + y        Left side y's cancelled out (-y + y = 0)

6 - 5 = 5 - 5 + y        Subtract 5 from both sides

6 - 5 = y        Right side cancelled out (5 - 5 = 0)

1 = y        Answer after left side simplified (6 - 5=1)

y = 1        Standard formatting puts variable on left

<u>Write the solution as an ordered pair</u> in the form (x, y).

The solution to the linear system is (3, 1).

<u>Check</u> if this is correct by <u>substituting x=3 and y=1</u> into both equations:

2x - y = 5

2(3) - 1 = 5     Simplify 2 times 3

6 - 1 = 5     Subtract

5 = 5     Same answer

LS = RS     Left side equals right side

Correct

5x + y = 16

5(3) + 1 = 16     Simplify 5 times 3

15 + 1 = 16     Add

16 = 16     Same answer

LS = RS     Left side equals right side

Correct.

Masteriza [31]3 years ago
6 0
7x= 21
X=3
Answer is 3! (:
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