What are the solutions to the system of equations?

y = 3x - 2

y = x²

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}

y = x² {second original equation}

y = 2² {substituted 2, in for x, into y = x²}

y = 4 {evaluated exponent}

(2,4) is a solution

y = x² {second original equation}

y = 1² {substituted 1, in for x, into y = x²}

y = 1 {evaluated exponent}

(1,1) is a solution

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.

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.

**- Algebra House**