A system of equations is given.

y = x² - 9

y = -2x - 1

What is one solution to the system?

y = x² - 9

y = -2x - 1

What is one solution to the system?

**A solution to a system of equations is the (x,y) coordinates where the two graphs intersect.**

**Since both, x² - 9 and -2x - 1 are equal to y, then set them equal to each other and solve for x.**

x² - 9 = -2x - 1

+2x + 1 +2x + 1

x² + 2x - 8 = 0 {added 2x and 1 to each side}

(x + 4)(x - 2) = 0 {factored into two binomials}

x + 4 = 0 or x - 2 = 0 {set each factor equal to zero}

x = -4 or x = 2 {solved each equation for x}

**Substitute both values for x into one of the two original equations to solve for y.**

__If x = -4,__

y = -2(-4) - 1 {substituted -4, in for x, into second original equation}

y = 8 - 1 {multiplied -2 by -4}

y = 7 {subtracted}

**(-4,7) is one solution**

__If x = 2,__

y = -2(2) - 1 {substituted 2, in for x, into second original equation}

y = -4 - 1 {multiplied -2 by 2}

y = -5 {subtracted}

**(2,-5) is one solution**

**(-4,7) and (2,-5) are two solutions to the equation.**They are the points of intersection of the straight line and the

parabola (as shown below)