Solve the following system of equations using the elimination method.

Question

2x−3y=14
, 4x+3y=10


(1 point)

Answer 1

To solve the system of equations using the elimination method, we start with the given equations:

1. $2x-3y=14$ (Equation 1)
2. $4x+3y=10$ (Equation 2)

First, we can eliminate $y$ by adding the two equations together. To do this, we can multiply Equation 1 by 1 (no change necessary) and Equation 2 by 1 (again, no change):

1. $2x-3y=14$
2. $4x+3y=10$

Now, we add the two equations:

$$(2x-3y)+(4x+3y)=14+10$$

This simplifies to:

$$6x=24$$

Next, we solve for $x$:

$$x=\frac{24}{6}=4$$

Now that we have $x$, we will substitute this value back into one of the original equations to solve for $y$. We'll use Equation 1:

$$2(4)-3y=14$$

This simplifies to:

$$8-3y=14$$

Now, we can isolate $y$:

$$-3y=14-8$$ $$-3y=6$$ $$y=\frac{6}{-3}=-2$$

Thus, the solution to the system of equations is:

$$x=4,y=-2$$

Final answer:

$(4,-2)$