Substitution Method to Solve Linear Equations

 

❓ Question

Solve the following pair of equations by the Substitution Method:

$$7x-15y=2$$
$$x+2y=3$$

---

🖼️ Solution Image

---

✍️ Short Concept

This question is based on:

👉 Pair of Linear Equations in Two Variables

👉 Substitution Method

👉 Solving Simultaneous Equations

---

🔷 Step 1 — Express One Variable

From

$$x+2y=3$$

we get

$$x=3-2y$$

---

🔷 Step 2 — Substitute into the Other Equation

Substitute $x=3-2y$ into

$$7x-15y=2$$
$$7(3-2y)-15y=2$$
$$21-14y-15y=2$$
$$21-29y=2$$
$$-29y=2-21$$
$$-29y=-19$$
$$y=\frac{19}{29}$$

---

🔷 Step 3 — Find the Value of x

Substitute

$$y=\frac{19}{29}$$

into

$$x=3-2y$$
$$x=3-2\left(\frac{19}{29}\right)$$
$$x=\frac{87-38}{29}$$
$$x=\frac{49}{29}$$

---

🔷 Step 4 — Verify the Answer

Substitute values into

$$7x-15y$$
$$=7\left(\frac{49}{29}\right)-15\left(\frac{19}{29}\right)$$
$$=\frac{343-285}{29}$$
$$=\frac{58}{29}$$
$$=2$$

LHS = RHS ✔

---

✅ Final Answer

$$\boxed{x=\frac{49}{29}}$$
$$\boxed{y=\frac{19}{29}}$$

Therefore, the solution of the pair of equations is:

$$\boxed{\left(\frac{49}{29},\frac{19}{29}\right)}$$

---

🚨 Common Mistakes

❌ Forgetting to substitute the entire expression $3-2y$ in place of $x$

❌ Sign errors while expanding $7(3-2y)$

❌ Not simplifying fractions correctly

---

✅ Final Takeaway

In the Substitution Method:

✔ Express one variable in terms of the other

✔ Substitute into the second equation

✔ Solve for one variable first

✔ Substitute back to find the other variable

---

📚 Related Topics

• Find Zeroes and Verify Relationship Between Coefficients
• Find Quadratic Polynomial from Sum and Product of Zeroes
• Quadratic Polynomial with Irrational Zeroes Explained