A system of equations is given.
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) Comments are closed.

Algebra 1 State Test Practice Archives
January 2020
