Questions: 6. We want to solve the following system of equations using the substitution method. Equation 1 y=5x-42 Equation 2 3x+4y=39 6a First solve for x.

Solution Steps

To solve the system of equations using the substitution method, we first use Equation 1, which already expresses \( y \) in terms of \( x \). We substitute this expression for \( y \) into Equation 2. This substitution will allow us to solve for \( x \).

We start with the two equations:

1. \( y = 5x - 42 \)
2. \( 3x + 4y = 39 \)

We substitute \( y \) from Equation 1 into Equation 2: \[ 3x + 4(5x - 42) = 39 \]

Now, we simplify the equation: \[ 3x + 20x - 168 = 39 \] Combining like terms gives: \[ 23x - 168 = 39 \]

Next, we isolate \( x \): \[ 23x = 39 + 168 \] \[ 23x = 207 \] \[ x = \frac{207}{23} = 9 \]

Final Answer