"Chapter 6 ReviewDirections: Complete the following sets of problems.Find the solution of ordered pairs for the following systems.1.y = -1/2x – 2 and 2x – y = 4Solution: solve for y in y=1/2x-2substitute y= -x/2-2solve for x in 5x/2+2=4 x-4/5substitute x=4/5 into y=-x/2-2 y=12/5therefore:x=4/5y=12/52. 3x – y = 2 and –y = 4x + 2 =Solutions for 3x-y=2 add y to both sides 3x=2+ydivide both sides by 3 x=2+y/3Solutions for -y=4x+2multiply both sides by -1 therefore: x=2+y/3y=-4x-23.1/3x – y = 1 and 1/4x – y = 1Solution: solve equation for the variable x=4y+4 (4y+4)-3y=3 y=-1x=4y=4use the y to solve the value the xx=4(-1)+4=0therefore: {x,y}={0,-1} Solve each system by graphing. Determine if the system is consistent orinconsistent.4.2x + 3y = 3 and 4x + 6y = -12Answer:consistent5.3x -2y = -1 and 2x – 4y = 2 Answer:inconsistent6.y = -1 and x = -2 Answer: inconsistent7. x –y = 1 and y = 2 consistent Answer: 8.3x + 3y = 21 and 3x + 4y = 24Answer: consistent9.3x + 2y = 5 and 9x + 6y = 12Answer: Inconsistent10.2x + y = -6 and x = -3Answer: ConsistentUse the substitution method to solve for the system of equations. If the solution isdependent or inconsistent, then identify them as such.11. .25x + 75y = 4 and x – y = 4 (.25x+75y=4) equation 1(x-y=4) equation 2 Solution: Swap equation 1 with equation 2x-y=4 .25x+75y=4therefore:x=4.03987 y=0.039867112. .5x + .5y = 5 and y = x + 2.5 Substitute y=x+2.5 into .5x+5y=5x+1.25=5solve for x in x+1.25=5 x=3.75 Substitute x=3.75 into y=x+2.5 y=6.35therefore: x=3.75 and y=6.3513. x + y = 2 and 1/5x – 1/3y = 2 Substitute x=2-y into 1/5x-1/3y=2 2(3-4y)/15=2solve for y in 2(3-4y)/15=2 y=-3substitute y into x=2-yx=5 therefore:x=5 and y=- 314. 2x – 3y = -3 and 2/3x – y = -1substitute y=1+2x/3 into 2x-2y=-3-3=3since -3=-3 is redundant information, this is a dependent systemSolve each system using the addition or addition-multiplication method wherenecessary. Check your solutions to see if they satisfy the equations.15. 2y = 41 – 5x and y = 17 – 2xSolution: 2y=41-5x y=17-2xy=-2x+172y=41-5x y=-2x+172(-2x+17)=41-5x therefore: x=7 and y=316.-4x + 7y = 9 and 2y = -5x -22 Solution: -4x+7y+-7=9+-7y (add b-7y to both sides) -4x=-7y+9-4x/-4=-7y+9/-4x=7/4y+-9/4substitute: 7/4y+-9/4 for x in 2y=-5x-222y=-5(7/4y+-9/4-222y=-35/4y+-43/4 (simplify both sides of the equations)2y+35/4y+-35/4y+-43/4+35/4y (add both sides by 35/4y)43/4y=43/4 (divide both sides by 43/4)y=-1substitute: -1 for y in x=7/4y+-9/4x=7/4(-1)+-9/4 X=-4therefore: x=-4 and y=-117. 3x + 2y = -3 and 2x + 3y = -2 solution: 3x + 2y+-2y=-3+2y (add -2 both sides)3x=-2y-33x/3=-2y-3/3 (divide both sides by 3)x=-2/3y-12x+2y =-22(-2y/3-1)+2y=-22/3y-2+2+-2+2 (add both sides by 2)2/3y/2/3=0/2/3y=0x=-2/3y(0) -1 therefore x=-1 and y=018. 3x + 4y = 0 and x + 4y = -2 Solution: 3(-4y-2)+4y=0-8y-6=0-8y-6+6=0+6 (add 6 both sides)-8y=6-8y/-8=6/-8y=-3/4x=-4(-3/4)-2x=1 therefore: x=1 and y= -3/419. 1/3 x + ½ y = 6 and 2x – y = 4Solution: 2x-y+-2x=4+-2x(add-2x both sides)-y=-2x+4-y/-1=-2x+4/-1 (divide both sides by -1)y=2x-41/3x+1/2(2x-4)=64/3x-2+2=6+24/3x=8x=6y=2x-4y=(2)(6)-4y=8therefore: x=6 and y=8Solve the system for each variable, and check your solutions20.x + 3y and z = 4x and x + y + z = 8Solution: x+4x+x=6x 3y+y=4y 1z+1z=2z+8z= 10z 21. x + y + z = 60 and x – z = y + 6 and y = 40 – x – 3z 2xsolution: x+-x+x+2x=3x y+y+40y=42y z+-z+-2z=-4z22. 2x+ y + 4z = 3 and x + 2y = 2z -3 and 4z + 3y = 0 Solution: 2x+x=3x y+2y+3y=6y4z+2z+4z=10z3+-3=023. x + y + z = 1 and 2x – y + 3z = 4.5 and 4x -5y – 5z = -0.5solution: x+2x+4x=7x y+-y+-5y=-6yz+3z+-5z=-3z1+4.5+-0.5=5Write a system of two equations for the following problem and solve.24. A metal alloy that is made up of 15% aluminum is combined with a metal alloythat is 35% aluminum. If the result is 400 Kilograms of 27.5% of aluminum alloy, thenhow much of each alloy was used?System: x+y=400 .15x+.35y=.275*400Solution:.35*(400-x)+.15x=.257*400 -139.85=0.275*400 Write a system with three equations for the following problem and solve.25. If the digits of a three-digit number are reversed in order, then the sum of thenew resulting number and the original number comes out to be 665. The difference ofthe two numbers is 297. The tens’ digit place is two times the hundreds’ place digit.What is the number? System: x+y=665 (1 equation) x-y=297(2 equation)solution: add 1and 2 equation2x=962y=x-297=184answer: x=481 "