Solve the system of two linear equations.

Question

−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)

Answer 1

To solve the system of the two linear equations:

1. $-3x-4y=-23$ (Equation 1)
2. $3x-5y=5$ (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. $-3x-4y=-23$
2. $3x-5y=5$

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

$$(-3x-4y)+(3x-5y)=-23+5$$

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

$$-4y-5y=-23+5$$

This simplifies to:

$$-9y=-18$$

Now, we solve for $y$:

$$y=\frac{-18}{-9}=2$$

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

$$3x-5(2)=5$$

This simplifies to:

$$3x-10=5$$

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:

$(5,2)$