Question

3k) Luna and Thomas also have overdue assignments to complete. Luna starts out with more overdue assignments than
Thomas but is completing more assignments per day than him. She ultimately completes her missing assignments
sooner than Thomas.
The equations below represent the rate at which they finish their assignments.
Thomas: 4x + 2y = 60
3x + y = 42
Use the Linear Combination Method to determine when Luna catches up to Thomas and has the same number of
assignments. How many remaining assignments do they have at that time?

1. The value of X is (3.5, -2)

### What is meant by solution of system?

A location that satisfies every equation in a system of linear equations is the system’s solution. You can graph a set of linear equations and find their points of intersection, or you can use algebra to figure out the variables.
We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The system will provide the solution at the point where the two lines intersect. The point where the two lines join is (-3, -4), which is where this equation system’s solution lies.
Given,
1. 3(4x – 7y = 28) → 12x – 21y = 84
-2(6x – 5y = 31) → -12x + 10y = -62
2. 12x – 21y = 84
+ -12x + 10y = -62
-11y = 22
3. y = -2
By simplifying
(3.5, -2)
Therefore The value of X is (3.5,-2)
The complete question is : Henrique began to solve a system of linear equations using the linear combination method. His work is shown below:
1. 3(4x – 7y = 28) → 12x – 21y = 84
-2(6x – 5y = 31) → -12x + 10y = -62
2. 12x – 21y = 84
+ -12x + 10y = -62
-11y = 22
3. y = -2
Complete the steps used to solve a system of linear equations by substituting the value of y into one of the original equations to find the value of x.
What is the solution to the system?