3x + y = 34
5x-y = 38 add the two equations
8x = 72
x = 9 then y = 7
x = -y^2 - 3y - 5 is a sideways parabola that opens to the left
to intersect at only one point, the line x = k must intersect at the vertex
arrange the equation to vertex form to find the vertex at -2.75 , -1.5 x = - 2.75
You must remember SOH CAH TOA SIN = OPP/HYP = 4/5 CSC = 1/SIN = 5/4
SEE IF YOU CAN DO THE REST
CAH COS = ADJ/HYP ETC ....
2x2 +28x +98 = (sqrt(2)x + sqrt (98))2
Initially j = 4/5 k or k = 5/4 j
Then
j - 5/8j + 108 = k + 5/8 j sub in red equation
3/8 j + 108 = 5/4j + 5/8 j
108 = 12/8 j
j = 72
2x - 4y = 9 + 3x - y. arrange to y = mx+b form m = slope parallel slope is ths same
3y =- x -9
y = -1/3 x - 3
the factors multiplied together = -18 added together = t
t
-18 1 -17
18 -1 17
-6 3 -3
6 -3 3
-9 2 -7
9 -2 7 multiply all of the t's together for your answer
Here is the first one....you try the similar second one....
a-3 = sqrt (5a-9) square both sides
a^2 - 6a + 9 = 5a-9 re-arrange
a^2 -11a +18 = 0
(a-9)(a-2) = 0 a = 9 or 2 test both answers.....you will find that only x = 9 works (throw out '2')
10 + 5 sqrt 3 and 10 - 5 sqrt 3
Initially
k = 1.25 j
then
k -96 = 1/2 (j+ 96) sub in the red equation
1.25j - 96 = 1/2 (j + 96)
.75 j = 144
j = 192 then k = 240
