Question

Describe how you would obtain an equation in one variable to solve the system by substitution. 12y = x - 15; -3x + 12y = 3.

a. Solve for x in the first equation and substitute into the second
b. Solve for y in the first equation and substitute into the second
c. Combine the two equations into one for substitution
d. Set both equations equal to each other and solve for x

Answer 1

To solve the system by substitution, solve for y in the first equation as y = (x - 15)/12. Then, substitute this into the second equation, simplify, and solve for x. After finding x, substitute it back into the first equation to find y. Here, option b is correct.

Step-by-step explanation:

To solve the system by substitution, we can use one of the provided methods. Here, option b is correct. First, solve for y in the first equation, and then substitute this value into the second equation.

• First, solve the first equation for y: 12y = x - 15, which gives us y = (x - 15)/12.
• Next, substitute this expression for y into the second equation: -3x + 12((x - 15)/12) = 3.
• Simplify and solve for x: -3x + x - 15 = 3, which simplifies to -2x = 18 and results in x = -9.
• Finally, substitute x back into the first equation to find y: 12y = -9 - 15, hence, y = -2.

In linear equations of the form y = a + bx, you typically solve for one variable in terms of the other and substitute this into the second equation to find the unique solution to the system.