Solve the system: 4x+y=9 x-2y=0?

4x+y=9
x-2y=0 => x=2y

4*2y+y=9
8y+y=9
9y=9
y=9/9
y=1

x=2y
x=2*1
x=2

Checking:
4x+y=9
4*2+1=9
8+1=9

x-2y=0
2-2*1=0
2-2=0

Good Luck

easy

eq1 4x + y = 9
eq2 x- 2y = 0

from 1: y=9-4x
sub into 2
x = 18 - 8x

x= 2

sub x=2 into 1

8 +y =9
y=1

if x -2y = 0 .... x= 2y

4(2y) + y = 9

9y = 9 ....y=1

if y =1 ...2y = 2 ... x = 2y = 2

Multiply eq. 1 by 2 and add the two eqs. together.
2(4x+y)+(x-2y)=2(9)+0
8x+2y+x-2y=18
9x=18
x=2
Use either eq. to solve for y.
4x+y=9
4(2)+y=9
8+y=9
y=1
(x,y)=(2,1)

4x+y=9
x-2y=0

Multiply the top equation by two and add the two together

8x+2y=18
x-2y=0

9x=18

x=2

x-2y=0
2-2y=0
2y=2
y=1

Therefore, x=2, y=1

Okay! ^-^ Thorough explanation provided!

4x + y = 9
x - 2y = 0

[Okay, the first thing to do is to choose a method to solve the system; let us do the elimination method, I will show you how it works]

1 (4x + y = 9)
4 (x - 2y = 0)

[Okay, from what I have typed above, I want both the x variables to have the same coefficient, which is why I chose small random numbers to distribute to both equations; let us see what happens next]

4x + y = 9
4x - 8y = 0

[Here is what happened; the top equation does not change, because multiplying the 1 to everything in the parenthesis keeps the numbers as is, but in the bottom equation, distributing 4 to everything in the parenthesis allowed the x variable to carry the same coefficient as the top equation, which is 4; let us continue]

4x + y = 9
- (4x - 8y = 0)

[I want to distribute a minus sign to the bottom equation, which will make dealing with both the 4x act as a subtraction problem; do not forget that the minus in front of the 8y will change to plus, and the zero at the end stays; let us continue]

4x + y = 9
-4x + 8y = 0

[Simply solve it like it was a basic math problem, like this]

9y = 9
y = 1

[We subtract both the 4x, which results in zero, add 8y to y, and add 9 and 0; divide 9 by 9, giving you the first answer, 1]

4x + y = 9 {Original top equation chosen}
4x + 1 = 9 {Substitute 1 for y}
4x = 8 {Subtract 1 from both sides}
x = 2 {Divide 4 by both sides, and the second answer is found}

(2,1) {This is your answer in an ordered pair}

Congratulations! ^-^ I'm sorry that I made this long, but I just want to provide examples that everyone can understand. I wish you good luck!

4x+y=9
x-2y=0
x=2y
4(2y)+y=9
8y+y=9
9y=9
y=1
x=2(1)=2

(x,y)=(2,1)

8x + 2 y = 18
x - 2 y = 0------ADD

9x = 18
x = 2

8 + y = 9
y = 1

x = 2 , y = 1

4x+y=9
x-2y=0

y=9-4x

x-2(9-4x)=0
x-18+8x=0
9x-18+18=0+18
x=2
2-2y=0
-2y=-2
y=1

Solve by using substitution.

4x + y = 9
x - 2y = 0

x - 2y = 0
x = (2y) ...... (1)

4x + y = 9

Substitute (1) for x.
4(2y) + y = 9
8y + y = 9
9y = 9
y = 9/9
y = 1

4x + y = 9

Substitute 1 for y.
4x + 1 = 9
4x = 9 - 1
x = 8/4
x = 2

∴ x = 2, y = 1