In rectangle FGHI, diagonals FH and GI intersect at E. G F E H I • IE = 3x + 4 • EG = 5x - 6 What is the length of FH ?
1 answer:
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Answer:
The solution to the system is ,
and
Step-by-step explanation:
Cramer's rule defines the solution of a system of equations in the following way:
,
and
where
,
and
are the determinants formed by replacing the x,y and z-column values with the answer-column values respectively.
is the determinant of the system. Let's see how this rule applies to this system.
The system can be written in matrix form like:
Then each of the previous determinants are given by:
Notice how the x-column has been substituted with the answer-column one.
Notice how the y-column has been substituted with the answer-column one.
Then, substituting the values:
Since both y squared and 6y have a common factor of y, can put that to the side and divide both the y squared and 6y to get the second step of the work shown above. Separate both the y on the outside of the parentheses and the numbers within the parentheses and set them both equal to 0 as shown in step 3 of the work shown above. Finally solve for y as you would normally. Those two number in step 4 should be your final answer.