Question

What is the solution to the system? Use substitution.

y=x+ 5
-2x+12 = y
A. (7,12)
B. (22/3,7/3)
C. (7/3,22/3)
D. not able to find

Answer 1

The solution to the system of linear equations is found by substituting the expression for y from the first equation into the second, solving for x, and then using the value of x to solve for y. The solution is (x = 7/3, y = 22/3), which is option C.

Step-by-step explanation:

The student is trying to solve a system of linear equations using the substitution method. The first equation given is y = x + 5, and the second equation is -2x + 12 = y. To use substitution, we replace y in the second equation with x + 5 from the first equation, resulting in -2x + 12 = x + 5. We then solve for x.

1. Substitute the value of y from the first equation into the second equation: -2x + 12 = x + 5.
2. Solve for x: -2x - x = 5 - 12 which simplifies to -3x = -7. Dividing both sides by -3 gives us x = 7/3.
3. Now, substitute x = 7/3 back into the first equation to find y: y = (7/3) + 5. Convert 5 to thirds: y = (7/3) + (15/3) which gives us y = 22/3.

The solution to the system is (x = 7/3, y = 22/3), which corresponds to option C.