Question

Solve the following system by elimination 3x+9y=9 -x+5y=-3

Answer 1

The solution to the system of equations 3x+9y=9 and -x+5y=-3 by elimination is x = 3, y = 0.

Step-by-step explanation:

To solve the system of equations by elimination, we can manipulate the equations to eliminate one of the variables. We have the given system of equations:

• 3x+9y=9
• -x+5y=-3

Let's multiply the second equation by 3 to make the coefficient of x in both equations have the same absolute value.

• -3(-x+5y) = -3(-3)

This gives us:

• 3x+9y = 9
• 3x-15y = 9

Now, if we add the first equation to the negative of the second equation, x will be eliminated:

• (3x+9y) - (3x-15y) = 9 - 9

Solving for y:

• 24y = 0
• y = 0

Substituting y = 0 into the first equation:

• 3x + 9(0) = 9
• 3x = 9
• x = 3

The solution to the system is x = 3, y = 0.

Answer 2

(x, y) = (1, -2/5)

Step-by-step explanation:

To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the two equations. In this case, we can eliminate y by multiplying the second equation by 3 and adding it to the first equation:

3(-x + 5y) = -3x + 15y = -9y + (-3)

3x + 9y = 9

Adding the two equations, we get:

6x = 6

Solving for x, we get:

x = 1

Now that we have the value of x, we can substitute it into either of the original equations to solve for y. Let’s use the second equation:

-x + 5y = -3

-(1) + 5y = -3

5y = -2

y = -2/5

Therefore, the solution to the system of equations 3x + 9y = 9 and -x + 5y = -3 is (x, y) = (1, -2/5).