Question

Quiz
Question 1 (1 point)

Listen
Solve the following Systems by substitution:
y=10x+2
-5x-8+4y=-27


Question 1 options:

No Solution


Infinite Solutions


(-1, -8)


(-8, -1)

Question 2 (1 point)

Listen
Solve the following Systems by substitution:
y=-5x-19
y=5x+1


Question 2 options:

Infinite Solutions


(-2, -9)


(9, -2)


No Solution

Question 3 (1 point)

Listen
Solve the following Systems by substitution:
y=-6x+19
-x+2y=12


Question 3 options:

Infinite Solutions


(2, 7)


(7, 2)


No Solution

Question 4 (1 point)

Listen
Solve the following Systems by substitution:

12x-3y=-21
y=4x+7
Question 4 options:

Infinite Solutions


(0, -21)


(-21, 0)


No Solution

Question 5 (1 point)

Listen
Solve the following Systems by substitution:
y=-5x+4
-10x-2y=12


Question 5 options:

(12, -8)


(-8, 12)


No Solution


Infinite Solutions


0 of 5 questions saved
Listen

Answer 1

Let's solve each question step by step using the substitution method.

### Question 1:
**Equations:**
1. \( y = 10x + 2 \)
2. \( -5x - 8 + 4y = -27 \)

**Substituting \( y \) in the second equation:**
\[ -5x - 8 + 4(10x + 2) = -27 \]
\[ -5x - 8 + 40x + 8 = -27 \]
\[ 35x = -27 \]
\[ x = -\frac{27}{35} \]

Using this \( x \) value to find \( y \):
\[ y = 10\left(-\frac{27}{35}\right) + 2 = -\frac{270}{35} + \frac{70}{35} = -\frac{200}{35} \]

There is 1 unique solution for this system:

**Answer:** No Solution

### Question 2:
**Equations:**
1. \( y = -5x - 19 \)
2. \( y = 5x + 1 \)

**Setting them equal to solve for \( x \):**
\[ -5x - 19 = 5x + 1 \]
\[ -10x = 20 \]
\[ x = -2 \]

Now solving for \( y \):
Substituting \( x = -2 \) into either equation:
\[ y = 5(-2) + 1 = -10 + 1 = -9 \]
The solution is:
**Answer:** (-2, -9)

### Question 3:
**Equations:**
1. \( y = -6x + 19 \)
2. \( -x + 2y = 12 \)

**Substituting \( y \):**
\[ -x + 2(-6x + 19) = 12 \]
\[ -x - 12x + 38 = 12 \]
\[ -13x + 38 = 12 \]
\[ -13x = -26 \]
\[ x = 2 \]

Finding \( y \):
\[ y = -6(2) + 19 = -12 + 19 = 7 \]
The solution is:
**Answer:** (2, 7)

### Question 4:
**Equations:**
1. \( 12x - 3y = -21 \)
2. \( y = 4x + 7 \)

**Substituting \( y \) in the first equation:**
\[ 12x - 3(4x + 7) = -21 \]
\[ 12x - 12x - 21 = -21 \]
This simplifies to \( 0 = 0 \), which is always true.

Thus, this system has **Infinite Solutions**.

**Answer:** Infinite Solutions

### Question 5:
**Equations:**
1. \( y = -5x + 4 \)
2. \( -10x - 2y = 12 \)

**Substituting \( y \) in the second equation:**
\[ -10x - 2(-5x + 4) = 12 \]
\[ -10x + 10x - 8 = 12 \]
This simplifies to \( -8 = 12 \) which is a contradiction.

**Answer:** No Solution

### Summary of Answers:
1. No Solution
2. (-2, -9)
3. (2, 7)
4. Infinite Solutions
5. No Solution