Question

Solving systems of equations

X-2y=0
Y=2x-3

Answer 1

x - 2y = 0
y = 2x - 3

You subsitute. Since, y = 2x - 3, then you fill what y equals in for the y on the top equation.

x - 2 (2x - 3) = 0 :Distribute

x - 4x + 6 = 0 :Combine Like Terms

-3x + 6 = 0 :Subtract the 6 over to the 0
-6 -6

(-3x = -6) ÷ -3 :Now, divide the whole equation by -3

x = 2

Then, you want to get y, so you fill in the x that you got before into the bottom equation.

y = 2 ( 2) - 3 :Now, multiply 2 × 2 (Because of PEMDAS)

y = 4 - 3

y = 1

Your final answer is:

(2, 1)

Answer 2

`\left \{ {{x-2y=0} \atop {y=2x-3}} \right. \\\\Substitute\ second\ equation\ to\ first:\\\\x-2(2x-3)=0\\x-4x+6=0\\-3x=-6\ \ \ \ \ |:-3\\x=2\\\\y=2\cdot2-3\\y=4-3=1\\\\ \left \{ {{y=1} \atop {x=2}} \right.`