Answer:
To summarize:
- The solution to the system of equations y = 5x + 4 and x + 12 = y is x = 2 and y = 14.
Explanation:
To solve the equations y = 5x + 4 and x + 12 = y, we can use the concept of substitution. Since both equations are equal to y, we can set them equal to each other and solve for x.
Substituting the expression for y from the first equation into the second equation, we have:
x + 12 = 5x + 4
Next, we can isolate the variable x by subtracting x from both sides:
12 = 5x - x + 4
Simplifying the equation, we get:
12 = 4x + 4
Subtracting 4 from both sides, we have:
8 = 4x
Finally, we divide both sides by 4 to solve for x:
x = 2
Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use the first equation:
y = 5(2) + 4
Simplifying the equation, we get:
y = 10 + 4
y = 14
So, the solution to the system of equations is x = 2 and y = 14.
To summarize:
- The solution to the system of equations y = 5x + 4 and x + 12 = y is x = 2 and y = 14.