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)

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)