Question

Solve the system of linear equations using the substitution method.

8x−13y=0
12x+3=y

Answer 1

To solve the given system of linear equations using the substitution method, isolate y in the second equation and substitute it into the first equation. Solve for x and then substitute x back into the original expression for y to find the values x = -39/148 and y = -1/4.

Step-by-step explanation:

To solve the system of linear equations using the substitution method, we start by looking at the equations given:

1. 8x - 13y = 0
2. 12x + 3 = y

From the second equation, we can isolate y to get y = 12x + 3. Now that we have y expressed in terms of x, we can substitute this expression into the first equation in place of y:

1. 8x - 13(12x + 3) = 0

Next, we expand and simplify the equation:

1. 8x - 156x - 39 = 0
2. -148x - 39 = 0
3. -148x = 39
4. x = -39/148

Once we have the value of x, we substitute it back into the expression for y:

1. y = 12(-39/148) + 3
2. y = -39/12 + 3
3. y = -13/4 + 3
4. y = -1/4

Thus, the solution to the system of linear equations is x = -39/148 and y = -1/4.