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
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.
Step 1: Substitute y in Equation 2
We start with the two equations:
y=5x−42
3x+4y=39
We substitute y from Equation 1 into Equation 2:
3x+4(5x−42)=39
Step 2: Simplify the Equation
Now, we simplify the equation:
3x+20x−168=39
Combining like terms gives:
23x−168=39