
3. Find the solution of the following systems of equations.
a.) . x+y=3
        2x-y=0
b.)  x-7y=-11
      5X+2y=-18

Let's solve each system of equations step by step.

### a) System of Equations:
\[
\begin{aligned}
x + y &= 3 \quad \text{(Equation 1)} \\
2x - y &= 0 \quad \text{(Equation 2)}
\end{aligned}
\]

**Step 1: Solve one of the equations for one variable.**

From Equation (2): 
\[
2x - y = 0 \implies y = 2x
\]

**Step 2: Substitute into the other equation.**

Substitute \( y = 2x \) into Equation (1):
\[
x + 2x = 3 \implies 3x = 3
\]
\[
x = 1
\]

**Step 3: Solve for the second variable.**

Substitute \( x = 1 \) into \( y = 2x \):
\[
y = 2(1) = 2
\]

So, the solution for system **a)** is:
\[
x = 1, \quad y = 2
\]

---

### b) System of Equations:
\[
\begin{aligned}
x - 7y &= -11 \quad \text{(Equation 3)} \\
5x + 2y &= -18 \quad \text{(Equation 4)}
\end{aligned}
\]

**Step 1: Solve one of the equations for one variable.**

From Equation (3): 
\[
x = 7y - 11
\]

**Step 2: Substitute into the other equation.**

Substitute \( x = 7y - 11 \) into Equation (4):
\[
5(7y - 11) + 2y = -18
\]
Expand:
\[
35y - 55 + 2y = -18 \implies 37y - 55 = -18
\]
\[
37y = 37 \implies y = 1
\]

**Step 3: Solve for the second variable.**

Substitute \( y = 1 \) into \( x = 7y - 11 \):
\[
x = 7(1) - 11 = 7 - 11 = -4
\]

So, the solution for system **b)** is:
\[
x = -4, \quad y = 1
\]

---

### Final Solutions:
- For system **a)**: \( x = 1, y = 2 \)
- For system **b)**: \( x = -4, y = 1 \)

Would you like more details on any of the steps?

---

### 5 Related Questions:
1. How can substitution help solve systems of equations?
2. What other methods can be used to solve systems of equations?
3. Can you explain how elimination works for solving systems of equations?
4. How do you check if a solution to a system of equations is correct?
5. How can systems of equations be applied in real-world problems?

**Tip:** When solving systems of equations, substitution is effective if one variable is already isolated or easy to isolate!

3. Find the solution of the following systems of equations.
a.) x + y = 3, 2x - y = 0
b.) x - 7y = -11, 5x + 2y = -18

Learn how to solve two systems of linear equations using the substitution method. This detailed step-by-step solution demonstrates key algebraic techniques for solving equations like x + y = 3, 2x - y = 0 and x - 7y = -11, 5x + 2y = -18. Suitable for students in Grades 8-10.

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