Warm Up2. Solve for a: 9a – 2b = c + 4a 3. Solve by graphing and state the solution4. a. Write the equation of the line b. Write the inequality of the line.
Warm Up5. If it takes eight carpenters (all working at the same time and rate) fifteen days to build a house, how long will it take for ten carpenters to build the same house? 8 carpenters • 15 days = 120 carpenter-days. Therefore 10x (x being the number of days)= 120. x = 12 days for 10 carpenters5. 1/3(3/5x + 18) = 3/4x +2/5
Review: Solve by Elimination Practice 1: y = x + 7 x + 2y = 5Practice 2: x - 3y = 7 3x +3y = 9
Solve: Elimination By Multiplying 0x + y = = 4 x + 0y 4 Like variables must be lined 2x + 3y = 9 under each other. We need to eliminate (get rid of) a variable.To simply add this time will not eliminate a variable. If there wasa –2x in the 1st equation, the x’s would be eliminated when weadd. So we will multiply the 1st equation by a – 2.
Solve: Elimination By Multiplying( X + Y = 4 ) -2 -2X - 2 Y = - 82X + 3Y = 9 2X + 3Y = 9 Now add the two equations Y=1 and solve. THEN----
Substitute your answer into either original equation andsolve for the second variable. X+Y=4 X +1=4 - 1 -1 X=3 Answer (3,1) Now check our answers in both equations--
Solve: By Substitution Recall that when we solve a point-slope formula, we end up in slope-intercept form. In much the same way, the substitution method is closely related to the elimination method.After eliminating one variable and solving for the other, wesubstitute the value of the variable back into the equation.For example: Solve 2x + 3y = -26 using elimination 4x - 3y = 2 What is the At this point we substitute -4 for x, value of x ? and solve for y. This is exactly what the substitution method is except it is done at the beginning.
Solve: By Substitution Example 1: y = 2x 4x - y = - 4Example 1: Substitute 2x for y in the 2nd equation y = 2x 4x - 2x = -4; 2x = -4; x = -2Then, substitute -2 for x in the first equation: y = 2(-2); y = -4Finally, plug both values in and check for equality. -4 = 2(-2); True; 4(-2) - (-4) = -4; -8 + 4 = -4; True
Solve: By SubstitutionExample 2: 3x + 5y = -7 x = 2y + 5Example 3: y = 2x - 1 6x - 3y = 7
Applying Systems of Equations Solve by Elimination.Example 1: The sum of two numbers is 52.The larger number is 2 more than 4 timesthe smaller number. Find both numbers.Example 1: -(x + y = -52 -x - y = 52) x+y=52 + _________ Rearrange x = 4y + 2 -4y = 2 -5y = -50 y = 10 x + 10 = 52; x = 42