Solve, using the substitution method. y + 2x = 7 14 – 4x = 2y A. The solution is (1, 5) B. The solution is (21, 0) C. There are an infinite number of solutions. D. There is no solution.
Mathematics · Middle School · Thu Feb 04 2021
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Let's solve the system of equations using the substitution method. The system of equations given are: 1) y + 2x = 7 2) 14 – 4x = 2y
Start with Equation 1 and solve for y: y = 7 - 2x
Now, take this expression for y and substitute it into Equation 2 where y is: 14 - 4x = 2(7 - 2x)
Simplify the equation by distributing the 2 on the right-hand side: 14 - 4x = 14 - 4x
As you can see, when you simplify both sides of the equation, you get the same expression (14 - 4x = 14 - 4x). This means the two lines represented by the equations are identical, and there is not just one solution to this system but instead an infinite number of solutions where the two lines overlap completely.
Thus, the correct answer is: C. There are an infinite number of solutions.