Question

Solve the following system of equations by the addition method:

5x - y = 6
-2x + 3y = -5
What is the value of the x-coordinate?
a) 3
b) 2
c) 1
d) -1

Answer 1

After manipulating the equations to eliminate the variable y by multiplying the first equation by 3, the system of equations simplifies to 13x = 13, resulting in x = 1, which is option (c).

Step-by-step explanation:

To solve the system of equations by the addition method, we aim to eliminate one variable so we can solve for the other. We have the following equations:

1. 5x - y = 6
2. -2x + 3y = -5

We need to manipulate the equations so that adding them eliminates one of the variables. To eliminate y, we can multiply the first equation by 3 and the second equation by 1 and then add them together:

1. (3)(5x - y) = (3)(6) -> 15x - 3y = 18
2. (-2x + 3y) = -5

Adding the equations together gives:

15x - 3y - 2x + 3y = 18 - 5

13x = 13

Divide both sides by 13 to isolate x:

x = 1

So, the value of the x-coordinate is 1, which corresponds to option (c).