Solve the system of equations by the addition method.
2x - 4y = 30
- 3x + 3y = - 21

x=−1 and y=−8

Step-by-step explanation:

2x−4y=30;−3x+3y=−21

Step: Solve2x−4y=30for x:

2x−4y+4y=30+4y(Add 4y to both sides)

2x=4y+30

2x

2

=

4y+30

2

(Divide both sides by 2)

x=2y+15

Step: Substitute2y+15forxin−3x+3y=−21:

−3x+3y=−21

−3(2y+15)+3y=−21

−3y−45=−21(Simplify both sides of the equation)

−3y−45+45=−21+45(Add 45 to both sides)

−3y=24

−3y

−3

=

24

−3

(Divide both sides by -3)

y=−8

Step: Substitute−8foryinx=2y+15:

x=2y+15

x=(2)(−8)+15

x=−1(Simplify both sides of the equation)

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)