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Question
Solve the system of equations.
5x+2y=14

x−6y=22
(1 point)
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,
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Answer 1

To solve the system of equations:

1. $5x+2y=14$ (Equation 1)
2. $x-6y=22$ (Equation 2)

We can solve it using substitution or elimination. Here, we will use substitution.

First, let’s solve Equation 2 for $x$:

$$x=6y+22$$

Now we can substitute $x$ in Equation 1:

$$5(6y+22)+2y=14$$

Expanding this gives us:

$$30y+110+2y=14$$

Combine like terms:

$$32y+110=14$$

Subtract 110 from both sides:

$$32y=14-110$$

$$32y=-96$$

Now, divide by 32:

$$y=\frac{-96}{32}=-3$$

Now we know $y$, we can substitute $y$ back into the equation for $x$:

$$x=6(-3)+22$$

$$x=-18+22$$

$$x=4$$

Thus, the solution to the system of equations is:

$$(x,y)=(4,-3)$$

So the final answer is:

$(4,-3)$