Question

In this system of equations, what is the value of y?

2x + y + 2z = 1
4x + 3z = -5
5y + 4z = 13

Answer 1

To find the value of y in the given system of equations, we can solve the system using the method of substitution.

Step-by-step explanation:

To find the value of y, we can solve the given system of equations using the method of substitution.

First, we can solve the second equation for z: 4x + 3z = -5 => 3z = -5 - 4x => z = (-5 - 4x)/3.

Next, we substitute the values of y and z in the first and third equations:

2x + y + 2((-5 - 4x)/3) = 14 => 6x + 3y - 10 - 8x = 42 => -2x + 3y = 52,

5y + 4((-5 - 4x)/3) = 13 => 15y - 20 - 16x = 39 => 15y - 16x = 59.

We now have a system of two equations with two variables:

-2x + 3y = 52,

15y - 16x = 59.

Solving this system of equations, we can determine the value of y.