Graph this system of equations and solve.
expr([ "+", [ "*", A1, "x" ], [ "*", B1, "y" ] ]) = C1
y = PRETTY_SLOPE_1 x + YINT_1
expr([ "+", [ "*", A2, "x" ], [ "*", B2, "y" ] ]) = C2
y = PRETTY_SLOPE_2 x + YINT_2
Drag the points to plot the system.
x = X
y = Y
Convert the first equation,
expr([ "+", [ "*", A1, "x" ], [ "*", B1, "y" ] ]) = C1,
to slope-intercept form.
y = PRETTY_SLOPE_1 x + YINT_1
The y-intercept for the first equation is YINT_1, so the first line
must pass through the point (0, YINT_1).
The slope for the first equation is decimalFraction(SLOPE_1, true, true).
So for every
abs(SLOPE_1_FRAC[0]) positions you move
down (because it's negative)up,
you must also move SLOPE_1_FRAC[1] positions to the right.
So for every
abs(SLOPE_1_FRAC[0]) positions you move
down (because it's negative)up,
you must also move SLOPE_1_FRAC[1] position to the right.
So for every
abs(SLOPE_1_FRAC[0]) position you move
down (because it's negative)up,
you must also move SLOPE_1_FRAC[1] positions to the right.
So for every
abs(SLOPE_1_FRAC[0]) position you move
down (because it's negative)up,
you must also move SLOPE_1_FRAC[1] position to the right.
SLOPE_1_FRAC[1] positions to the right and
abs(SLOPE_1_FRAC[0]) positions
downup
from (0, YINT_1) is
(SLOPE_1_FRAC[1], YINT_1 + SLOPE_1_FRAC[0]).
SLOPE_1_FRAC[1] positions to the right and
abs(SLOPE_1_FRAC[0]) position
downup
from (0, YINT_1) is
(SLOPE_1_FRAC[1], YINT_1 + SLOPE_1_FRAC[0]).
SLOPE_1_FRAC[1] position to the right and
abs(SLOPE_1_FRAC[0]) positions
downup
from (0, YINT_1) is
(SLOPE_1_FRAC[1], YINT_1 + SLOPE_1_FRAC[0]).
SLOPE_1_FRAC[1] position to the right and
abs(SLOPE_1_FRAC[0]) position
downup
from (0, YINT_1) is
(SLOPE_1_FRAC[1], YINT_1 + SLOPE_1_FRAC[0]).
Graph the blue line so it passes through
(0, YINT_1) and
(SLOPE_1_FRAC[1], YINT_1 + SLOPE_1_FRAC[0]).
Convert the second equation,
expr([ "+", [ "*", A2, "x" ], [ "*", B2, "y" ] ]) = C2,
to slope-intercept form.
y = PRETTY_SLOPE_2 x + YINT_2
The y-intercept for the second equation is YINT_2, so the second line
must pass through the point (0, YINT_2).
The slope for the second equation is decimalFraction(SLOPE_2, true, true).
So for every
abs(SLOPE_2_FRAC[0]) positions you move
down (because it's negative)up,
you must also move SLOPE_2_FRAC[1] positions to the right.
So for every
abs(SLOPE_2_FRAC[0]) positions you move
down (because it's negative)up,
you must also move SLOPE_2_FRAC[1] position to the right.
So for every
abs(SLOPE_2_FRAC[0]) position you move
down (because it's negative)up,
you must also move SLOPE_2_FRAC[1] positions to the right.
So for every
abs(SLOPE_2_FRAC[0]) position you move
down (because it's negative)up,
you must also move SLOPE_2_FRAC[1] position to the right.
SLOPE_2_FRAC[1] positions to the right and
abs(SLOPE_2_FRAC[0]) positions
downup
from (0, YINT_2) is
(SLOPE_2_FRAC[1], YINT_2 + SLOPE_2_FRAC[0]).
SLOPE_2_FRAC[1] positions to the right and
abs(SLOPE_2_FRAC[0]) position
downup
from (0, YINT_2) is
(SLOPE_2_FRAC[1], YINT_2 + SLOPE_2_FRAC[0]).
SLOPE_2_FRAC[1] position to the right and
abs(SLOPE_2_FRAC[0]) positions
downup
from (0, YINT_2) is
(SLOPE_2_FRAC[1], YINT_2 + SLOPE_2_FRAC[0]).
SLOPE_2_FRAC[1] position to the right and
abs(SLOPE_2_FRAC[0]) position
downup
from (0, YINT_2) is
(SLOPE_2_FRAC[1], YINT_2 + SLOPE_2_FRAC[0]).
Graph the green line so it passes through
(0, YINT_2) and
(SLOPE_2_FRAC[1], YINT_2 + SLOPE_2_FRAC[0]).
The solution is the point where the two lines intersect.
The lines intersect at x = X, y = Y.