Question

Solving Simultaneous Equations Using Substitution Practice answers

Answer 1

Sure! I'll provide you with a set of simultaneous equations and then demonstrate how to solve them using substitution. After that, you can practice solving similar equations, and I can provide the answers if you'd like.

### Example Problem:

Solve the following system of equations using substitution:

1. \( y = 2x + 3 \)
2. \( 3x + 2y = 12 \)

### Step-by-step Solution:

1. **Substitute for \(y\)** in the second equation using the first equation:
\[
3x + 2(2x + 3) = 12
\]

2. **Expand and simplify**:
\[
3x + 4x + 6 = 12
\]
\[
7x + 6 = 12
\]

3. **Isolate \(x\)**:
\[
7x = 12 - 6
\]
\[
7x = 6
\]
\[
x = \frac{6}{7}
\]

4. **Substitute \(x\) back** into the first equation to find \(y\):
\[
y = 2\left(\frac{6}{7}\right) + 3
\]
\[
y = \frac{12}{7} + \frac{21}{7}
\]
\[
y = \frac{33}{7}
\]

### Solution:
The solution to the system of equations is:
\[
x = \frac{6}{7}, \quad y = \frac{33}{7}
\]

---

### Practice Problems:

Try solving these pairs of simultaneous equations using substitution:

1.
- \( y = 3x + 1 \)
- \( 2x + y = 10 \)

2.
- \( y = 4x - 2 \)
- \( 5x + 3y = 20 \)

3.
- \( y = -2x + 5 \)
- \( 4x + 2y = 10 \)

### Answers:

Once you have tried solving them, here are the answers to check your work:

1. \( x = 2, \, y = 7 \)
2. \( x = 2, \, y = 6 \)
3. \( x = 0, \, y = 5 \)

Feel free to reach out if you need any help or explanations regarding the practice problems!