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Furkat [3]
2 years ago
6

Find the solution to the system of equations: 7x-8y=-23 7x-7y=-14

Mathematics
1 answer:
Vinil7 [7]2 years ago
4 0

Answer:

Solutions: x = 7, y = 9;  or (7, 9)

Step-by-step explanation:

Given the following systems of linear equations:

7x - 8y = -23

7x - 7y = -14

Since the coefficients of x in the given system have the same sign, we could use the process of elimination by subtracting the two equations.

    7x - 8y = -23

<u> -   7x - 7y = -14     </u>

             -y = -9  

Divide both sides by -1 to solve for y:

\frac{-y}{-1} =  \frac{-9}{-1}

y = 9

Substitute the value of y into either one of the given equations to solve for x:

7x - 7y = -14

7x - 7(9) = -14

7x - 63 = -14

Add 63 to both sides:

7x - 63 + 63 = -14 + 63

7x = 49

Divide both sides by 7 to solve for x:

\frac{7x}{7} = \frac{49}{7}

x = 7

Double-check whether x = 7 and y = 9 are valid solutions to the given system:

x = 7, y = 9:

<h3>7x - 8y = -23</h3>

7(7) - 8(9) = -23

49 - 72 = -23

-23 = -23 (True statement).

<h3>7x - 7y = -14</h3>

7(7) - 7(9) = -14

49 - 63 = -14

-14 = -14 (True statement).

Therefore, the solution to the given systems of linear equations are x = 7, and y = 9, or (7, 9).

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