Digital GardenMathsLinear AlgebraLinear EquationsLinear Equations An equation is linear if it has the following form: a1x1+a2x2+…+anxn+b=0a_1x_1 + a_2x_2 + \ldots + a_nx_n + b = 0a1x1+a2x2+…+anxn+b=0 Visualizing Equations 1 Variable 2 Variables slope-intercept form: y=mx+by = mx + by=mx+b n Variables Solving Equations System of Linear Equations ∣a11x1+a12x2+…+a1nxn=b1a21x1+a22x2+…+a2nxn=b2⋮am1x1+am2x2+…+amnxn=bm∣\begin{vmatrix} a_{11}x_1 + a_{12}x_2 + \ldots + a_{1n}x_n = b_1 \\ a_{21}x_1 + a_{22}x_2 + \ldots + a_{2n}x_n = b_2 \\ \vdots \\ a_{m1}x_1 + a_{m2}x_2 + \ldots + a_{mn}x_n = b_m \end{vmatrix}a11x1+a12x2+…+a1nxn=b1a21x1+a22x2+…+a2nxn=b2⋮am1x1+am2x2+…+amnxn=bm Solving Systems of Linear Equations Substitution Method Addition/Subtraction MethodPolynomialsGaussian Elimination