Question

Solve for x and y in the following equations using the substitution elimination method: 6x - 7y = 5 and 3x + y = 7.

a) x = 3, y = 2
b) x = 2, y = 3
c) x = 1, y = 2
d) x = 2, y = 1

Answer 1

To solve the system of equations using the substitution elimination method, we first solve one equation for one variable and substitute it into the other equation. Then we solve for the remaining variable. The solution to the system of equations 6x - 7y = 5 and 3x + y = 7 is x = 2 and y = 1.

Step-by-step explanation:

To solve the system of equations 6x - 7y = 5 and 3x + y = 7 using the substitution elimination method, we can start by solving one equation for one variable and substituting it into the other equation. Let's solve the second equation for y:

3x + y = 7

y = 7 - 3x

Now substitute this value of y into the first equation:

6x - 7(7 - 3x) = 5

Expand and simplify:

6x - 49 + 21x = 5

Combine like terms:

27x - 49 = 5

Add 49 to both sides:

27x = 54

Divide by 27:

x = 2

Now substitute this value of x back into the second equation:

3(2) + y = 7

6 + y = 7

Subtract 6 from both sides:

y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1. So the correct answer is d) x = 2, y = 1.