Solve the system of equations 3y + 2z = 12 and y - z = 9.

Solution:

A linear equation is an equation that is written for two different variables.

This equation will be a linear combination of these two variables, and a constant can be present.

Surprisingly, when any linear equation is plotted on a graph, it will necessarily produce a straight line.

Given, the system of equations are

3y + 2z = 12 --- (1)

y - z = 9 --- (2)

We have to find the solution of the system of equations.

From (2), y = 9 + z

Put the value of y in (1)

3(9 + z) + 2z = 12

27 + 3z + 2z = 12

5z = 12 - 27

5z = -15

z = -15/5

z = -3

Put z = -3 in (2)

y - (-3) = 9

y + 3 = 9

y = 9 - 3

y = 6

Therefore, the solutions to the equations are y = 6 and z = -3.

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Solve the system of equations 3y + 2z = 12 and y - z = 9.

Summary:

The solutions to the system of equations 3y + 2z = 12 and y - z = 9 are y = 6 and z = -3.