Question

Help me please!!!! quick please :(

Answer 1

No solutions: y=5x+4 and y=5x-2

One solution: y=-2x+3 and y=0.5x-7, y=2x-7 and y=5x+4, y=-2x+3 and y=2x-1

Infinitely many solutions: 3y=-12x+6 and y=-4x+2

Explanation:

The goal is to get x alone if possible to see if there is one solution. If x cancels out, then there can be infinite solutions or no solution. These problems can be solved by substitution. For example, in the first equation, both equations are equal to y. Therefore, y can be substituted by one of the equations.

y=-2x+3

y=0.5x-7 Set the equations equal to each other.

-2x+3=0.5x-7 Simplify by adding 7 to both sides and adding 2x to both

sides. You must do the operation to both sides to keep

the equations equal to each other.

10=2.5x Next, divide by 2.5 to get x alone.

x=4 Now, plug this into one of the original equations to find

y.

y=-2(4)+3 Solve. -2*4=-8, -8+3=-5

y=-5 Your solution as an x,y pair is (4,-5)

y=2x-7

y=5x+4 Follow the same process as the previous system.

2x-7=5x+4 Subtract 2x from both sides and subtract 4 from both

sides.

-11=3x Divide by 3 on both sides.

x=
`-(11)/(3)` This is the result. It's in fraction form because the

answer is a repeating decimal.

y=2(
`-(11)/(3)` )-7 Plug into an equation.

y=
`-(43)/(3)` Although the solution doesn't include "nice" integers,

this equation still has one solution, which is (
`-(11)/(3)`,
`-(43)/(3)`).

3y=-12x+6 --> y=-4x+2

y=-4x+2 For this system, note that it starts with 3y. The first

step is to divide both sides of the first equation by 3 to

make the first equation equal to y. -12x/3=-4x and

6/3=2. Then proceed, using the same method as

before.

-4x+2=-4x+2 You can either stop here or continue. This system

automatically has infinite solutions because anything

is equal to itself. Or you can continue by adding 4x to

both sides and subtracting 2 from both sides.

0=0 This will be your result, which is true.

y=-2x+3

y=2x-1 Continue with substitution.

-2x+3=2x-1 Add 2x and 1 to both sides.

4=4x Divide by 4

x=1 Plug into an equation.

y=2(1)-1 Solve.

y=0 The solution is (1,0)

y=5x+4

y=5x-2 More substitution!

5x+4=5x-2 Subtract 5x from both sides.

4=-2 Unlike an earlier system, this statement is NOT true.

Therefore, this system has no solutions.