Question

Use substitution. What is the solution to the system of equations? Use the drop-down menus to explain your answer. y = 12 x + 2 2y = x + 4 The system of equations has Choose... . The two equations represent Choose... .

Answer 1

The solution to the system of equations is x = 50 and y = 602.

Explanation:

To solve the system of equations using substitution, we can start by solving one of the equations for one variable in terms of the other. Let's solve the first equation, y = 12x + 2, for y in terms of x:

y = 12x + 2

Now we can substitute this expression for y into the second equation, 2y = x + 4, and solve for x:

2(12x + 2) = x + 4

24x + 4 = x + 4

23x = 0

x = 0/23

x = 50

Now that we have solved for x, we can substitute this value into either equation to solve for y. Let's use the first equation, y = 12x + 2:

y = 12(50) + 2

y = 602

Therefore, the solution to the system of equations is x = 50 and y = 602.

Regarding the drop-down menu options:

- The system of equations has one solution. (This is the correct option, as there is only one set of values for x and y that satisfy both equations.)
- The two equations represent two lines. (This is also correct, as each equation represents a line in the xy-plane.)