Question

Solve the system of equations using elimination.

−
5
x
−
3
y
=
−
13
4
x
+
2
y
=
12
−5x−3y=−13
4x+2y=12



What is the LCM of the x values?
20


What is the LCM of the y values?
6


(b)
Write your equivalent equations.

First equation:


Second equation:

(c)
What operation did you use to elimnate?
addition


(d)
When solving,

x
=
x=




y
=
y=

Answer 1

Fill in the blanks
¿Qué
parece la sorpresa, niño? ¿Te gusta? Señor, ¿qué
parece a usted?
le
te

Answer 2

To solve the given system of equations using elimination, we'll follow these steps:

### Given Equations:
1. \(-5x - 3y = -13\) (Equation 1)
2. \(4x + 2y = 12\) (Equation 2)

### Step 1: Make the coefficients of \(y\) the same.

To eliminate \(y\), we can multiply Equation 1 by \(2\) (to get the coefficient of \(y\) as \(-6\)) and Equation 2 by \(3\) (to get the coefficient of \(y\) as \(6\)). This gives us:

**First equation multiplied by 2:**
\[
2(-5x - 3y) = 2(-13) \\
-10x - 6y = -26 \quad (Equation 1')
\]

**Second equation multiplied by 3:**
\[
3(4x + 2y) = 3(12) \\
12x + 6y = 36 \quad (Equation 2')
\]

### Step 2: Write the equivalent equations.
(a) First Equation:
\[
-10x - 6y = -26
\]

(b) Second Equation:
\[
12x + 6y = 36
\]

### Step 3: Add the two equations.
Now we will add Equation 1' and Equation 2':
\[
(-10x - 6y) + (12x + 6y) = -26 + 36
\]
This simplifies to:
\[
(2x + 0y) = 10 \\
2x = 10
\]

Now, divide both sides by \(2\):
\[
x = 5
\]

### Step 4: Substitute \(x\) back to find \(y\).
Use the value of \(x\) in either original equation (let's use Equation 2):
\[
4(5) + 2y = 12 \\
20 + 2y = 12 \\
2y = 12 - 20 \\
2y = -8 \\
y = -4
\]

### Final Solutions:
- \(x = 5\)
- \(y = -4\)

### LCM Values:
(a) The LCM of the x-values is:
\[
\text{LCM}(5) = 5
\]

(b) The LCM of the y-values is:
\[
\text{LCM}(-4) = 4
\]

### Final Result Summary:
- (b) First equation: \(-10x - 6y = -26\)
- (b) Second equation: \(12x + 6y = 36\)
- (c) The operation used to eliminate: **addition**
- (d) When solving,
- \(x = 5\)
- \(y = -4\)

Answer 3

The completed sentences would be:

¿Qué **te** parece la sorpresa, niño? ¿Te gusta? Señor, ¿qué **le** parece a usted?

- "te" is the informal second person singular pronoun (you, familiar).
- "le" is the formal third person singular pronoun (you, formal).

If you have any more questions or need further assistance, feel free to ask!