Question

Give me two linear equations using the substitution method

Answer 1

Sure! Let's consider the following two linear equations:

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

We can solve these equations using the substitution method. Here's how to do it step-by-step:

### Step 1: Substitute the value of \( y \) from the first equation into the second equation.

From equation 1, we have:
\[
y = 2x + 3
\]

Now we substitute this expression for \( y \) into equation 2:
\[
3x + 2(2x + 3) = 12
\]

### Step 2: Simplify and solve for \( x \).

Distributing the 2:
\[
3x + 4x + 6 = 12
\]
Combining like terms gives:
\[
7x + 6 = 12
\]

Now, subtract 6 from both sides:
\[
7x = 6
\]

Finally, divide by 7:
\[
x = \frac{6}{7}
\]

### Step 3: Substitute \( x \) back into the first equation to find \( y \).

Using \( y = 2x + 3 \):
\[
y = 2\left(\frac{6}{7}\right) + 3
\]
This simplifies to:
\[
y = \frac{12}{7} + \frac{21}{7} = \frac{33}{7}
\]

### Final Result

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

Thus, the ordered pair \(\left(\frac{6}{7}, \frac{33}{7}\right)\) represents the intersection point of the two lines represented by the equations.