Solve using the elimination method. Show your work. If the system has no solution or an infinite number of

Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
x + 8y = 14
-3x + 4y = 0

3x + 24y = 42
-3x + 4y = 0---------ADD

28y = 42

y = 42/28 = 3/2

x + 12 = 14
x = 2

x = 2 , y = 3/2

Pleased to help----thank you.

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x + 8y = 14------------->equation 1
-3x + 4y = 0------------>equation 2

Multiplying the second equation by 2 we have
-6x+8y=0------------>equation 3

Subtracting equation 3 from equation 1 we have
x+8y=14
6x-8y=0
----------------
7x=14
or, x=2

Putting x=2 in equation 1we have
2+8y=14
or, 8y=14-2
or, 8y=12
or, y=12/8
or, y=1.5

Therefore, the required solution is x=2 and y=1.5

Hope this helps!!!

Multiply the top equation by three

Pretend the equations are an addition problem, add the equation on top to the one on the bottom.

Solve for y using the resulting equation (x should be gone)

Plug in the y value that you got into one of the original eqations to solve for x.

x+8y=14---------------------------------…
-3x+4y=0------------------------------…

Multiply equation (1) by -3
-3x-24y=-42
-3+4y-28y=-42 since -3x+4y=0
-28y=-42
y=42/28=1.5
x=8*1.5=14
x-14-12=2
x=2,y=1.5

elimination
X+8y=14
+(-3x+4y=0)
-2x+12y=14
2x=12y-14
X=6y-7
(6y-7)+8y=14
14y-7=14
14y=21
y=2/3
x=-3