What are the solutions to the system of equations?
y = 3x  2 y = x²
x² = 3x  2 {substituted x², in for y, into first equation}
x²  3x + 2 = 0 {subtracted 3x and added 2 to each side} (x  2)(x  1) = 0 {factored into two binomials} x  2 = 0 or x  1 = 0 {set each factor equal to 0} x = 2 or x = 1 {solved each equation for x} If x = 2 y = x² {second original equation} y = 2² {substituted 2, in for x, into y = x²} y = 4 {evaluated exponent} (2,4) is a solution If x = 1 y = x² {second original equation} y = 1² {substituted 1, in for x, into y = x²} y = 1 {evaluated exponent} (1,1) is a solution (2,4) and (1,1) are solutions to the system of equations. When graphed, y = 3x  2 is a straight line, and y = x² is a parabola. The solutions are the points of intersection of the straight line and the parabola. Comments are closed.

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