2-Substitution+method

The Substitution Method

**To solve with the substitution method first you must get one variable from one of the equations alone.** Ex.) x+2y=2 3x+2y=2  x= -2y+2

**Next you will substitute what the variable equals into the other equation and solve for the other variable.** Ex.) 3x+4y= -4 Write equation  3(-2y+2)+4y= -4 Substitute -2y+2 in for x  -6y+6+4y= -4 Solve for y  -2y+6= -4  -2y= -10  y=5

**Then you will substitute the value from step two into the first revised equation. ** Ex.) x= -2y+2 Write equation  x= -2(5)+2 Substitute 5 in for y  x= -10+2 Solve for x  x= -8

<span style="color: #22bcf7; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**So the solution for the system is the ordered pair (-8, 5)** <span style="color: #22bcf7; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> <span style="color: #22bcf7; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> <span style="color: #22bcf7; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**EXAMPLES:** <span style="color: #22bcf7; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**<span style="color: black; line-height: 14.25pt; margin-bottom: 0in; margin-left: 0in; margin-right: 0in; margin-top: 0in;">2x - 3y = 5 ** <span style="color: #22bcf7; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">** x= 4y-2 -- (move to second equation and substitute) 2x - 3y = 5  ** <span style="color: #22bcf7; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">** X = 36/5 – 2 **
 * 2 (4y-2) - 3y = 5 **
 * -- (Distribute) 8y + - 4 + -3y = 5 **
 * -- (Add like terms) 5y + - 4 = 5 **
 * -- (Isolate variable) +4 = +4 **
 * -- (Isolate variable) 5y = 9 ** <span style="color: #22bcf7; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">** -- (Divide) y = 9/4 ** <span style="color: #22bcf7; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">
 * <span style="color: #22f744; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Then you substitute "Y" into the equation (you use the opposite equation.) For example, we used "2x - 3y = 5." So now, were going to use x = 4y - 2.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">x = 4 (9/4) - 2 **
 * X = 26/5 **