Systems of Equations

hi.

there are three ways we know how to solve systems of equations

substitution
{x+y = 10, x-y = 4} {equation 1, equation 2}

x=10-y {solve for x in equation 1}

(10-y)-y=4 {substitute 'solution for x in equation 1' into equation 2}
10-2y=4 {simplify}
2y=6 {simplify}
y=3 {solve for y}
x+(3)=10 {plug y into equation 1}
x=7 {solve for x}

solution: (7, 3)



elimination

{x+y = 10, x-y = 4} {equation 1, equation 2}

{x+y=10 {add (or subtract) equations, eliminating one variable}
{x-y=4
-2y=-6 {determine new equation}

y=3 {solve for y}
x+(3)=10 {plug y into equation 1}
x=7 {solve for x}

solution: (7, 3)


graphing

{x+y = 10, x-y = 4} {equation 1, equation 2}

plug both into calculator

find where the graphs intersect each other

solution: (7, 3)


fun stuff i know

bye.