Match the equation on the left with the appropriate ordered pair solution on the right.

(1, -4)

Ask by Bradley Erickson. in the United States

Jan 24,2025

Question

Match the equation on the left with the appropriate ordered pair solution on the right. $$ \begin{array}{l} 2 x+3 y=-10 \ -3 x-5 y=1 \ -2 x+y=10 \end{array} $$ (1, -4) $$ (-3,4) $$

UpStudy AI · Accepted Answer

Let's determine which ordered pair $$(x, y)$$ satisfies each equation by substituting the values into the equations.

### Given Ordered Pairs:
1. $$(1, -4)$$
2. $$(-3, 4)$$

### Equations:
1. $$2x + 3y = -10$$
2. $$-3x - 5y = 1$$
3. $$-2x + y = 10$$

---

### **1. $$2x + 3y = -10$$**

- **Substitute $$(1, -4)$$:**
  $$
  2(1) + 3(-4) = 2 - 12 = -10 \quad \checkmark
  $$
  
- **Substitute $$(-3, 4)$$:**
  $$
  2(-3) + 3(4) = -6 + 12 = 6 \neq -10 \quad \text{✗}
  $$

**Conclusion:** $$(1, -4)$$ satisfies this equation.

---

### **2. $$-3x - 5y = 1$$**

- **Substitute $$(1, -4)$$:**
  $$
  -3(1) - 5(-4) = -3 + 20 = 17 \neq 1 \quad \text{✗}
  $$
  
- **Substitute $$(-3, 4)$$:**
  $$
  -3(-3) - 5(4) = 9 - 20 = -11 \neq 1 \quad \text{✗}
  $$

**Conclusion:** Neither $$(1, -4)$$ nor $$(-3, 4)$$ satisfies this equation.

---

### **3. $$-2x + y = 10$$**

- **Substitute $$(1, -4)$$:**
  $$
  -2(1) + (-4) = -2 - 4 = -6 \neq 10 \quad \text{✗}
  $$
  
- **Substitute $$(-3, 4)$$:**
  $$
  -2(-3) + 4 = 6 + 4 = 10 \quad \checkmark
  $$

**Conclusion:** $$(-3, 4)$$ satisfies this equation.

---

### **Final Matching:**
- **$$2x + 3y = -10$$** matches with **$$(1, -4)$$**
- **$$-2x + y = 10$$** matches with **$$(-3, 4)$$**

The equation $$ -3x - 5y = 1 $$ has **no matching ordered pair** among the given options.

**Summary:**
$$
\begin{align*}
2x + 3y &= -10 &\leftrightarrow&\ (1,\ -4) \
-2x + y &= 10 &\leftrightarrow&\ (-3,\ 4) \
-3x - 5y &= 1 &\leftrightarrow&\ \text{No match}
\end{align*}
$$
$$(1, -4)$$ matches $$2x + 3y = -10$$ and $$(-3, 4)$$ matches $$-2x + y = 10$$.

Match the equation on the left with the appropriate ordered pair solution on the right.

(1, -4)

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Match the equation on the left with the appropriate ordered pair solution on the right. (1, -4)