2y-x=5
x2+y2-25=0

solve the system by the substitution method

(- 5, 0), (3, 4)

Step-by-step explanation:

Given the 2 equations

2y - x = 5 → (1)

x² + y² - 25 = 0 → (2)

Rearrange (1) expressing x in terms of y

x = 2y - 5 → (3)

Substitute x = 2y - 5 into (2)

(2y - 5)² + y² - 25 = 0 ← expand parenthesis and simplify

4y² - 20y + 25 + y² - 25 = 0

5y² - 20y = 0 ← factor out 5y from each term

5y(y - 4) = 0

Equate each factor to zero and solve for y

5y = 0 ⇒ y = 0

y - 4 = 0 ⇒ y = 4

Substitute these values into (3) for corresponding values of x

y = 0 : x = 0 - 5 = - 5 ⇒ (- 5, 0)

y = 4 : x = 8 - 5 = 3 ⇒ (3, 4)

y=0 or 4, x=-5 or 3

Step-by-step explanation:

First make one unknown in the first equation the subject of the formula.

2y-x=5 will become:x=2y-5

Then in the second equation, wherever there is x we substitute it with 2y-5

(2y-5)²+y²-25=0         (2y-5)(2y-5)+y²-25=0

opening the brackets gives: 4y²-10y-10y+25+y²-25=0

5y²-20y=0

Factorizing the equation we get the following:

y(5y-20)=0

y=0 or

5y-20=0

5y=20

y=4

Thus y=0 or 4

Substitute 0 and 4 for y in any of the equations provided.

Picking the first equation and starting with y=0

2(0)-x=5

x=-5

Using y=4

2(4)-x=5

x=3

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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