solve.1)y=5y+1 and -2y+10=3. 2)-x+2y=3 and 3x-6y=-9. 3) x+3y=5 and 5x+6y=-2.

Question

solve the following equations. show work.substitution,addition,or graphing.

Answer 1

Substitution method :

1).

The system of equations are y = 5y + 1 and - 2y +10 = 3.

The above system of equations have only one variable that is y, so system of equations has no solution.

Solve the each equation separately for y.

Solve the equation 1 : y = 5y + 1.

y - 5y = 1

- 4y = 1

y = - 1/4.

Solve the equation 2 : - 2y + 10 = 3.

- 2y = 3 - 10

- 2y = - 7

y = 7/2.

The solution set {y | y = - 1/4 and y = 7/2}.

2).

The system of equations are - x + 2y = 3 and 3x - 6y = - 9.

Solve equation 1: - x + 2y = 3 for x, since the x has a coefficient of - 1.

- x = 3 - 2y

x = 2y - 3.

Substitute the value x = 2y - 3 in equation 2: 3x - 6y = - 9 and solve for y.

3(2y - 3) - 6y = - 9

6y - 9 - 6y = - 9

- 9 = - 9.

The above statement is true, so the system of has infinitely many solutions.

3).

The system of equations are x + 3y = 5 and 5x + 6y = - 2.

Solve equation 1 : x + 3y = 5 for x, since the x has a coefficient of 1.

x + 3y = 5

x = 5 - 3y.

Substitute the value x = 5 - 3y in equation 2: 5x + 6y = - 2 and solve for y.

5(5 - 3y) + 6y = - 2

25 - 15y + 6y = - 2

25 - 9y = - 2

- 9y = - 27

y = 3.

Substitute the value y = 3 in x = 5 - 3y and solve for x.

x = 5 - 3(3)

x = 5 - 9

x = - 4.

Solution of the system is x = - 4 and y = 3.