Question

Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given in Example 3. {4x+12y = 0 {12x+4y = 160

Answer 1

To solve the given system of equations:

{4x + 12y = 0
{12x + 4y = 160

We can use the method of elimination or substitution. Let's use the method of elimination:

Multiply the first equation by 3 and the second equation by -1 to create opposite coefficients for x:

{12x + 36y = 0
{-12x - 4y = -160

Adding the two equations together eliminates the x term:

0 + 32y = -160
32y = -160
y = -160/32
y = -5

Substituting the value of y back into the first equation:

4x + 12(-5) = 0
4x - 60 = 0
4x = 60
x = 60/4
x = 15

Therefore, the solution to the system of equations is x = 15 and y = -5, or in ordered-pair form, (15, -5).

Answer 2

To solve the system of equations 4x + 12y = 0 and 12x + 4y = 160, we can use the method of elimination. By multiplying Equation 1 by 3 and Equation 2 by 1, we can eliminate the x variable and solve for y. Substituting the value of y back into one of the original equations gives us the value of x.

Step-by-step explanation:

To solve the given system of equations:

Equation 1: 4x + 12y = 0

Equation 2: 12x + 4y = 160

We can start by multiplying Equation 1 by 3 and Equation 2 by 1, so that the coefficients of x or y will cancel each other out when we add the equations together:

3(4x + 12y) = 3(0) ---> 12x + 36y = 0

1(12x + 4y) = 1(160) ---> 12x + 4y = 160

Now, we can subtract the second equation from the first equation:

(12x + 36y) - (12x + 4y) = 0 - 160

32y = -160

Simplifying further:

y = -160 / 32

y = -5

Now, we can substitute the value of y back into one of the original equations:

4x + 12(-5) = 0

4x - 60 = 0

4x = 60

x = 60 / 4

x = 15

Therefore, the solution to the system of equations is (15, -5).