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.

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