What is the solution set of the system? Use substitution. 3x + 2y = 7 and y = -3x + 11

Solution:

Given: Linear equations are given:

3x + 2y = 7 --- (1)

y = -3x + 11 --- (2)

Let us use the substitution method to solve the system of linear equations of two variables.

Substtitue (2) in (1)

3x + 2( -3x + 11) = 7

Now we have obtained a linear equation of one variable. Let us isolate the variable x and solve for it.

3x + 2( -3x + 11) = 7

3x-6x+22 = 7

-3x = 7 -22

3x = 15

x = 5

Substitute the value of x in equation (2)

3x + 2y = 7

3(5) + 2y = 7

2y = 7-15

y = -8/2 =-4

Therefore, the solution set of the system is (5,-4).

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What is the solution set of the system? Use substitution. 3x + 2y = 7 and y = -3x + 11

Summary:

The solution set of the system using substitution for 3x + 2y = 7 and y = -3x + 11 is ((5,-4).