Question

Use substitution. What is the solution to the system of equations? Use the drop-down menus to explain your answer.

y =x+2
2y=x+4

Answer 1

The solution to the system of equations using substitution is x = 0 and y = 2 by substituting the expression for y from the first equation into the second, simplifying, and solving for x.

Step-by-step explanation:

To find the solution to the system of equations using the substitution method, we can follow these steps:

1. Identify the first equation where y is already isolated: y = x + 2.
2. Substitute the expression for y from the first equation into the second equation, replacing y with x + 2 in 2y = x + 4.
3. Rewrite the second equation by substituting y which gives us 2(x + 2) = x + 4.
4. Expand and simplify the equation to solve for x: 2x + 4 = x + 4.
5. Subtract x from both sides resulting in x = 0.
6. Substitute the value of x back into the first equation to find the corresponding value for y: y = 0 + 2 which simplifies to y = 2.

Therefore, the solution to the system is x = 0 and y = 2.