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