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Airida [17]
3 years ago
8

Solve the system by the substitution method. Show your work. 2y - x = 5, x2 + y2 - 25 = 0

Mathematics
1 answer:
Anna71 [15]3 years ago
8 0
Subsitution

2y-x=5
minus 2y both sides
-x=5-2y
times -2 both sides
x=2y-5

subsitute 2y-5 for x in other equation

(2y-5)²+y²-25=0
expand
4y²-20y+25+y²-25=0
5y²-20y=0
factor
5y(y-4)=0
set to zero

5y=0
y=0

y-4=0
y=4


subsitute back

for y=0
x=2y-5
x=2(0)-5
x=-5
one solution is (-5,0)

for x=4
x=2y-5
x=2(4)-5
x=8-5
x=3
one solution is (3,4)




the 2 soltuions are (-5,0) and (3,4)
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in a coordinate plane the midpoint of AB is (4,-3) and A has coordinate (1,5). if B has coordinate (x,y) find the value x+y​
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Answer:

Please check the explanation.

Step-by-step explanation:

The midpoint (a, b) of line joining points (x₁, y₁) and (x₂, y₂)

a = x₁ + x₂ / 2

b = y₁ + y₂ / 2

Given that the midpoint of AB is (4, -3).

i.e. (a, b) = (4, -3)

Given that A has coordinate (1, 5).

i.e. (x₁, y₁) = (1, 5)

We have to determine the coordinates of B.

i.e. (x₂, y₂) = B

Thus,

4 = (1 + x₂)/2

(1 + x₂) = 4 × 2

1 + x₂ = 8

x₂ = 7

and

-3 = (5 + y₂)/2

(5 + y₂) = -3 × 2

5 + y₂ = -6

y₂ = -11

so (x₂, y₂) = (7, -3) = B

Thus, the coordinates of B = (x₂, y₂)  = (7, -3)

Therefore,

x₂ + y₂ = 7 + (-3)

          = 7 - 3

          = 4

Hence, the value of x₂ + y₂ = 4

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3 years ago
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