Question

Find any three solutions to the system:

1.5y+x=−0.5
2x+3y=−1

Answer 1

y=1,x=-2 so (-2,1)

x=1, y=-1 so (1,-1)

x=2.5, y=-2 so (2.5,-2)

Explanation:

1.5y+x=−0.5, 2x+3y=−1 are the given equations.

If we were to multiple the first equation my 2 we would get

2(1.5y+x)=-0.5

3y+2x=-1

Meaning the two equations are the same so if you find a pair of numbers that works for one of theses equations it works for both.

Solutions:

y=1,x=-2 so (-2,1)

x=1, y=-1 so (1,-1)

Finally

x=2.5, y=-2 so (2.5,-2)

Hope this helps

Answer 2

Answer:
(1, -1), (4, -3), and (7, -5) because the system has infinitely many solutions

Explanation:
In order to find solutions to the system, we can choose a variable to cancel out and solve for the remaining variable. Then to find solutions for the variable we decided to cancel out, we plug in the initial variable and solve the equation. To simplify what I am saying, if we cancel out variable y, we solve for variable x and then use the value of x to find variable y.

Let's solve for y:
2x + 3y = -1
x + 1.5y = -0.5

Multiply the second equation by -2 in order to cancel out the x variable when we add them together.
2x + 3y = -1
-2(x + 1.5y = -0.5)

2x + 3y = -1
-2x - 3y = 1

Add them together and simplify
2x - 2x + 3y - 3y = -1 + 1
0x + 0y = 0
0 = 0

Because the solution yielded "0=0" in which both the x- and y-variables were canceled out, the answer to this system is infinitely many solutions because they are essentially the same line.

So we can plug in any number for x or y in either equation, solve, and list it as a solution to the system.
Example:
x = 1 x = 4 x = 7
2(1) + 3y = -1 2(4) + 3y = -1 2(7) + 3y = -1
2 + 3y = -1 8 + 3y = -1 14 + 3y = -1
2 - 2 + 3y = -1 - 2 8 - 8 + 3y = -1 - 8 14 - 14 + 3y = - 1 - 14
3y = -3 3y = - 9 3y = -15
y = - 1 y = -3 y = -5

(1, -1) (4, -3) (7, -5)

These three ordered pairs are examples of solutions to the system.