Start by seeing where the lines go. They cross (intersect) at (1, -1). We can use this to check later.
Now for slope: green is -4/2 = -2
pink is 4/2 = 2
Now we can create the equations
Let's make green = g(x) and pink = p(x)
if we use y = mx + b, then the green has a y-intercept (b) of +1
So g(x) = -2x + 1
pink has a y-intercept of -3, so p(x) = 2x - 3
Now let's plug n play: put our solutions x into each equation and confirm that it makes the y = -1
g(x) = -2x + 1 = -2(1) + 1 = -2+1 = -1
p(x) = 2x - 3 = 2(1) - 3 = 2-3 = -1
✔ YES THEY ARE CONFIRMED
Answer:
i tried on a calculator and it gave me 211.125
2x+3(2x-4y)+8y-2
2x+6x-12y+8y-2
8x-12y+8y-2
8x-4y-2
So, this creates a triangle once again. If we imagine a slide, the slide itself would be the hypotenuse of the triangle, then if there's a ladder leading up to the slide, that would be the vertical length we're looking for. The feet across the ground would be the distance from the bottom of the slide to the bottom of the ladder.
We can use the Pythagorean theorem to find the missing side length, as this would create a right triangle. | 8^2 + b^2 = 10^2 | 64 + b^2 = 100 | b^2 = 36 | b = 6 feet | The slide is 6 feet high at its highest point.
Use subsiution]
y=-3x+5
subsitute -3x+5 for y in second equation
5x-4(-3x+5)=-3
distribute
5x+12x-20=-3
add like terms
17x-20=-3
add 20 to both sides
17x=17
divide both sides by 17
x=1
now subsitute 1 for x
y=-3x+5
y=-3(1)+5
y=-3+5
y=2
x=1
y=2