Solve the system of two linear equations.

−3x−4y=−23

3x−5y=5
(1 point)
Responses

(−5, 2)
left parenthesis negative 5 comma 2 right parenthesis

(−5,−2)
left parenthesis negative 5 comma negative 2 right parenthesis

(5, 2)
left parenthesis 5 comma 2 right parenthesis

(5,−2)

1 answer

To solve the system of the two linear equations:

  1. 3x4y=23 (Equation 1)
  2. 3x5y=5 (Equation 2)

We can use either the substitution method or the elimination method. In this case, we will use the elimination method.

First, we can multiply Equation 2 by 1 to already make it easier to eliminate x:

  1. 3x4y=23
  2. 3x5y=5

Next, we'll add both equations together to eliminate x:

(3x4y)+(3x5y)=23+5

The 3x and 3x will cancel each other out:

4y5y=23+5

This simplifies to:

9y=18

Now, we solve for y:

y=189=2

Now that we have y=2, we can substitute this value back into Equation 2 to find x:

3x5(2)=5

This simplifies to:

3x10=5

Now, we’ll add 10 to both sides:

3x=15

Dividing by 3 gives:

x=5

So the solution to the system of equations is:

(x,y)=(5,2)

Therefore, the answer is:

(5,2)

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