Question

Quiz
Question 1 (1 point)

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Solve by substitution:

4x+y=1
5x-2y=-15

Question 1 options:

(-1, 5)


No Solution


(5, -1)


Infinite Solutions

Question 2 (1 point)

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Solve by substitution:
5x+2y=8
x+3y=-14

Question 2 options:

Infinite Solutions


(4, -6)


(-6, 4)


No Solution

Question 3 (1 point)

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Solve by substitution:

3x+4y=-24
5x+y=-23

Question 3 options:

(-4, -3)


Infinite Solutions


(-3, -4)


No Solution

Question 4 (1 point)

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Solve by substitution:

3x-y=-27
2x+3y=4

Question 4 options:

No Solution


Infinite Solutions


(-7, 6)


(6, -7)

Question 5 (1 point)

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Solve by substitution:
9x+2y=-14
-7x+y=16


Question 5 options:

(-2, 2)


(2, -2)


No Solution


Infinite Solutions


0 of 5 questions saved
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Answer 1

Let's solve each of the given systems of equations one by one using the substitution method.

### Question 1
**Equations:**
1. \( 4x + y = 1 \)
2. \( 5x - 2y = -15 \)

**Step 1:** Solve the first equation for \( y \):
\[ y = 1 - 4x \]

**Step 2:** Substitute into the second equation:
\[ 5x - 2(1 - 4x) = -15 \]
\[ 5x - 2 + 8x = -15 \]
\[ 13x - 2 = -15 \]
\[ 13x = -13 \]
\[ x = -1 \]

**Step 3:** Substitute \( x \) back to find \( y \):
\[ y = 1 - 4(-1) = 1 + 4 = 5 \]

**Solution:** \( (-1, 5) \)

---

### Question 2
**Equations:**
1. \( 5x + 2y = 8 \)
2. \( x + 3y = -14 \)

**Step 1:** Solve the first equation for \( y \):
\[ 2y = 8 - 5x \]
\[ y = 4 - \frac{5}{2}x \]

**Step 2:** Substitute into the second equation:
\[ x + 3(4 - \frac{5}{2}x) = -14 \]
\[ x + 12 - \frac{15}{2}x = -14 \]
\[ x - \frac{15}{2}x = -14 - 12 \]
\[ -\frac{13}{2}x = -26 \]
\[ x = 4 \]

**Step 3:** Substitute \( x \) back to find \( y \):
\[ y = 4 - \frac{5}{2}(4) = 4 - 10 = -6 \]

**Solution:** \( (4, -6) \)

---

### Question 3
**Equations:**
1. \( 3x + 4y = -24 \)
2. \( 5x + y = -23 \)

**Step 1:** Solve the second equation for \( y \):
\[ y = -23 - 5x \]

**Step 2:** Substitute into the first equation:
\[ 3x + 4(-23 - 5x) = -24 \]
\[ 3x - 92 - 20x = -24 \]
\[ -17x - 92 = -24 \]
\[ -17x = 68 \]
\[ x = -4 \]

**Step 3:** Substitute \( x \) back to find \( y \):
\[ y = -23 - 5(-4) = -23 + 20 = -3 \]

**Solution:** \( (-4, -3) \)

---

### Question 4
**Equations:**
1. \( 3x - y = -27 \)
2. \( 2x + 3y = 4 \)

**Step 1:** Solve the first equation for \( y \):
\[ y = 3x + 27 \]

**Step 2:** Substitute into the second equation:
\[ 2x + 3(3x + 27) = 4 \]
\[ 2x + 9x + 81 = 4 \]
\[ 11x + 81 = 4 \]
\[ 11x = -77 \]
\[ x = -7 \]

**Step 3:** Substitute \( x \) back to find \( y \):
\[ y = 3(-7) + 27 = -21 + 27 = 6 \]

**Solution:** \( (-7, 6) \)

---

### Question 5
**Equations:**
1. \( 9x + 2y = -14 \)
2. \( -7x + y = 16 \)

**Step 1:** Solve the second equation for \( y \):
\[ y = 7x + 16 \]

**Step 2:** Substitute into the first equation:
\[ 9x + 2(7x + 16) = -14 \]
\[ 9x + 14x + 32 = -14 \]
\[ 23x + 32 = -14 \]
\[ 23x = -46 \]
\[ x = -2 \]

**Step 3:** Substitute \( x \) back to find \( y \):
\[ y = 7(-2) + 16 = -14 + 16 = 2 \]

**Solution:** \( (-2, 2) \)

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### Final Answers:
1. \( (-1, 5) \)
2. \( (4, -6) \)
3. \( (-4, -3) \)
4. \( (-7, 6) \)
5. \( (-2, 2) \)