Solve for x and y using elimination.
\color{BLUE}{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1}
\color{GREEN}{expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) = C2}
x = X
y = Y
We can eliminate x by adding the equations together when the x coefficients have opposite signs.
Add the equations together. Notice that the terms expr(["*", A1, "x"]) and expr(["*", A2, "x"]) cancel out.
expr(["*", B1 * MULT1 + B2 * MULT2, "y"]) = C1 * MULT1 + C2 * MULT2
\dfrac{expr(["*", B1 * MULT1 + B2 * MULT2, "y"])}{\color{BLUE}{B1 * MULT1 + B2 * MULT2}} = \dfrac{C1 * MULT1 + C2 * MULT2}{\color{BLUE}{B1 * MULT1 + B2 * MULT2}}
\color{ORANGE}{y = Y}
Now that you know \color{ORANGE}{y = Y}, plug it back into \thinspace \color{BLUE}{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1}\thinspace to find x.
\color{BLUE}{expr(["*", A1, "x"]) + B1-}\color{ORANGE}{(Y)}\color{BLUE}{= C1}
expr(["+", ["*", A1, "x"], B1 * Y]) = C1
expr(["+", ["*", A1, "x"], B1 * Y])\color{BLUE}{SIGN_1abs( B1 * Y )} = C1\color{BLUE}{SIGN_1abs( B1 * Y )}
expr(["*", A1, "x"]) = C1 - B1 * Y
\dfrac{expr(["*", A1, "x"])}{\color{BLUE}{A1}} = \dfrac{C1 - B1 * Y}{\color{BLUE}{A1}}
\color{red}{x = X}
You can also plug \color{ORANGE}{y = Y} into \thinspace \color{GREEN}{expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) = C2}\thinspace and get the same answer for x:
\color{GREEN}{expr(["*", A2, "x"]) + B2-}\color{ORANGE}{(Y)}\color{GREEN}{= C2}
\color{red}{x = X}
Solve for x and y using elimination.
\color{BLUE}{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1}
\color{GREEN}{expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) = C2}
x = X
y = Y
We can eliminate y by adding the equations together when the y coefficients have opposite signs.
Add the equations together. Notice that the terms expr(["*", B1, "y"]) and expr(["*", B2, "y"]) cancel out.
expr(["*", A1 * MULT1 + A2 * MULT2, "x"]) = C1 * MULT1 + C2 * MULT2
\dfrac{expr(["*", A1 * MULT1 + A2 * MULT2, "x"])}{\color{BLUE}{A1 * MULT1 + A2 * MULT2}} = \dfrac{C1 * MULT1 + C2 * MULT2}{\color{BLUE}{A1 * MULT1 + A2 * MULT2}}
\color{red}{x = X}
Now that you know \color{red}{x = X}, plug it back into \thinspace \color{BLUE}{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1}\thinspace to find y.
\color{BLUE}{A1-}\color{red}{(X)}\color{BLUE}{ + expr(["*", B1, "y"]) = C1}
expr(["+", A1 * X, ["*", B1, "y"]]) = C1
A1 * X\color{BLUE}{SIGN_1abs( A1 * X )} + expr(["*", B1, "y"]) = C1\color{BLUE}{SIGN_1abs( A1 * X )}
expr(["*", B1, "y"]) = C1 - A1 * X
\dfrac{expr(["*", B1, "y"])}{\color{BLUE}{B1}} = \dfrac{C1 - A1 * X}{\color{BLUE}{B1}}
\color{ORANGE}{y = Y}
You can also plug \color{red}{x = X} into \thinspace \color{GREEN}{expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) = C2}\thinspace and get the same answer for y:
\color{GREEN}{A2-}\color{red}{(X)}\color{GREEN}{ + expr(["*", B2, "y"]) = C2}
\color{ORANGE}{y = Y}