The system of equations x + 2y = 6 and x – 4y = 0 is graphed below. What is the solution to the system of equations?

Mathematics

1 answer:

blagie [28]3 years ago

7 0

Step-by-step explanation:

$x + 2y = 6....(1) \\ \\ x - 4y = 0\\ \implies \: x = 4y....(2)\\ \\ from \: equations \: (1) \: and \: (2) \\ 4y + 2y = 6 \\ \therefore \: 6y = 6 \\ \\ \therefore \: y = \frac{6}{6} \\ \\ \huge \red{ \boxed{ \therefore \: y = 1}} \\ \\ substituting \: y = 1 \: in \: equation \: (2) \\ \\ x = 4y \\ \\ \therefore \: x = 4 \times 1 \\ \\ \huge \orange{ \boxed{\therefore \: x = 4 }} \\ \\ \therefore \: (x, \: \: y) = (4, \: \: 1) \\ is \: the \: required \: solution. \\$

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Find the midpoint of the segment with the following endpoints.<br> (8,5) and (0, -1)

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Answer:

(4,2)

Step-by-step explanation:

$Midpoint =\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(8,\:5\right),\:\\\left(x_2,\:y_2\right)=\left(0,\:-1\right)\\\\=\left(\frac{0+8}{2},\:\frac{-1+5}{2}\right)\\\\= (\frac{8}{2} , \frac{4}{2} )\\\\Simplify\\=\left(4,\:2\right)$