Solving Equations Using Substitution Practice

Question

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

x−6y=22
(1 point)
(
,
)

Answer 1

To solve the system of equations using substitution, we have the following equations:

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

Step 1: Solve one of the equations for one variable

Let's solve Equation 2 for $x$:

$$x=6y+22$$

Step 2: Substitute this expression into the other equation

Now we substitute $x$ in Equation 1:

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

Step 3: Distribute and simplify

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

Combine like terms:

$$32y+110=14$$

Step 4: Solve for $y$

Subtract 110 from both sides:

$$32y=14-110$$

$$32y=-96$$

Now divide by 32:

$$y=-3$$

Step 5: Substitute $y$ back to find $x$

Now, we substitute $y=-3$ back into the equation we derived for $x$:

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

$$x=-18+22$$

$$x=4$$

Final Solution

The solution to the system of equations is:

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

So the answer is:

$(4,-3)$