Please Help, Geometry Work due Tomorrow

1) x= 7

2)a. x=8, x=1

b.x=4,x=-1

3)(5,2)

Step-by-step explanation:

problem 1:

1) Distribute

4(x-5)=x+1

4x-20=x+1

2) Add 20 to both sides of the equation

4x-20=x+1

4x-20+20=x+1+20

3) Simplify

*Add the numbers

4x=x+21

4) Subtract x from both sides of the equation

4x=x+21

4x-x=x+21-x

5) Simplify

*Combine like terms

3x=21

6) Divide both sides of the equation by the same term.

3x=21

3x/3=21/3

7) Simplify

*Cancel terms that are in both the numerator and denominator

*Divide the numbers

Result: x=7

problem 2:

a

1) Use the sum-product pattern

Identify a, b, and c in your equation and then find two numbers that when multiplied together equal c and when added together equal b.

x²-9x+8=0

2) Factor

* Write your equation in factored form

(x-8)(x-1)=0

3) Create two separate equations

*set each factor equal to 0

x-8=0

x-1=0

4) solve

*rearrange and isolate the variable to find each solution

x=8

x=1

b.

1) move terms to the left side

2x²+7x-4=x²+10x

2x²+7x-4-(x²+10x)=0

2) distribute

2x²+7x-4=x²+10x

2x²+7x-4-x²-10x=0

3) combine like terms

2x²+7x-4-x²-10x=0

1x²+7x-4-10x=0

4) Multiply by 1

1x²+7x-4-10x=0

x²+7x-4-10x=0

5) combine like terms

x²+7x-4-10x=0

x²-3x-4=0

6) Use the sum-product pattern

Identify a, b, and c in your equation and then find two numbers that when multiplied together equal c and when added together equal b.

x²-3x-4-0

7) Factor

Write your equation in factored form

(x-4)(x+1)=0

8) Create two separate equations

Set each factor equal to zero

x-4=0

x+1=0

9) Solve

Rearrange and isolate the variable to find each solution

x=4

x= -1

-=

problem 3:

x+4y=13

x-y-3

multiplying this one by -1

x+4y=13

-x+y=-3

0x+5y=10

5y=10

y=10/2

y=2

since we know that

x-y=3

x-(2)=3

x=5

(5,2)