Question

2y + x = -15 , x=3y substitution method

Answer 1

To solve the system of equations 2y + x = -15 and x = 3y using the substitution method, substitute x from the second equation into the first, and then simplify and solve for y, finally substituting back to find x.

Step-by-step explanation:

The student is working on a system of equations problem, which is a concept in algebra, a branch of mathematics. The substitution method is one technique to solve such systems. In the given equations, 2y + x = -15 and x = 3y, the student can substitute x from the second equation into the first, resulting in 2y + (3y) = -15. Combining like terms gives 5y = -15. Dividing both sides by 5 yields y = -3. Substituting this value back into the second equation gives x = 3(-3), so x = -9. Plotting these values in a graph, we would see the intersection of the lines represented by the two equations at the point (-9, -3).

Answer 2

x = -9, y = -3.

As an ordered pair it is (-9, -3).

Step-by-step explanation:

Substitute x = 3y in equation 1:

2y + 3y = -15

5y = -15

y = -15/5

y = -3.

Now find x by plugging y = -3 in x = 3y:

x = 3*-3 = -9.

Check the answer in equation 1:

2(-3) + -9

= -6 - 9

= -15 Correct.