Question

Solve the system of equations using substitution:

2x + y = 8
3x - 2y = 1
a) x = 3, y = 2
b) x = 2, y = 4
c) x = 4, y = 0
d) x = 1, y = 6

Answer 1

To solve the system of equations using substitution, we solve one equation for one variable and substitute it into the other equation. The solution to the given system of equations is x = 17/7 and y = 10/7.

Step-by-step explanation:

To solve the system of equations using substitution, we will solve one equation for one variable and substitute it into the other equation. Let's solve the first equation for y:

2x + y = 8

y = 8 - 2x

Now, substitute this expression for y into the second equation:

3x - 2(8 - 2x) = 1

Simplify and solve for x:

3x - 16 + 4x = 1

7x - 16 = 1

7x = 17

x = 17/7

Now, substitute this value of x back into the first equation to solve for y:

2(17/7) + y = 8

34/7 + y = 8

y = 8 - 34/7

y = 10/7

Therefore, the solution to the system of equations is x = 17/7 and y = 10/7. None of the given options (a, b, c, d) is correct.