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.

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

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Solution Steps

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

Step 1: Substitute y y in Equation 2

We start with the two equations:

  1. y=5x42 y = 5x - 42
  2. 3x+4y=39 3x + 4y = 39

We substitute y y from Equation 1 into Equation 2: 3x+4(5x42)=39 3x + 4(5x - 42) = 39

Step 2: Simplify the Equation

Now, we simplify the equation: 3x+20x168=39 3x + 20x - 168 = 39 Combining like terms gives: 23x168=39 23x - 168 = 39

Step 3: Solve for x x

Next, we isolate x x : 23x=39+168 23x = 39 + 168 23x=207 23x = 207 x=20723=9 x = \frac{207}{23} = 9

Final Answer

The solution for x x is \\(\boxed{x = 9}\\).

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