REVIEW SYSTEMS OF EQUATIONS TYPES OF SOLVING SYSTEMS OF EQUATIONS 1.GRAPHING 2.SUBSTUTION 3.ELIMINATION

Integers!!! Same signs add keep sign Different signs subtract numbers take sign of “bigger” number OROR Type in calc!! Make sure you type on what you see!! Can’t do both

Solving a system of equations by graphing. Let's summarize! There are 3 steps to solving a system using a graph. Step 1: Graph both equations. Step 2: Do the graphs intersect? Step 3: Check your solution. Graph using slope and y – intercept. Be sure to use a ruler and graph paper! This is the solution! LABEL the solution! Substitute the x and y values into both equations to verify the point is a solution to both equations.

Graph the equations. Where do the lines intersect? (2, 0) 2x + y = 4 y = -2x + 4 y = x – 2

Solving a system of equations by Substitutesubstitution Step 1: Solve an equation for one variable. Step 2: Substitute Replace ONLY variable beings substituted for with ( ) Step 3: Solve the equation. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Pick the easier equation. The goal is to get y= ; x= ; a= ; etc. Put the equation solved in Step 1 into the other equation. Get the variable by itself. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations.

Ex1) x + y = 6 y = 2 + x x + (2 + x) = 6 2x + 2 = x = 4 x =2 The solution is (1, 4). What do you think the answer would be if you graphed the two equations? x+ y = 6 ( 2) + y = 6 -2 = -2 y = 4 (2) + (4) = 6 ✔ (4) = 2 + (2) ✔

Solving a system of equations by elimination using addition and subtraction. Step 1: Line up variables Step 2: Determine which variable to eliminate. Step 3: Add the equations. Step 4: Plug back in to find the other variable. Step 5: Check your solution. x’s under x’s and y’s under y’s and constants under constants Look for variables that have the same coefficient and different signs. Solve for the variable. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations.

3 ) 2x +2 y = 14 -4x - 2y = -6 -2x = 8 x = -4 2x+ 2y = 14 2(-4) +2y = y= 14 y = 11 2(-4) + 2(11) = 14 ✔ -4(-4) -2(11) = -6 ✔ +8 = + 8 2y= 22