4.1 systems of equations

determine if the replacement values make the equation true 3x-4y+2z=5 ; x=1, y=2, z=5

plug the numbers in 3(1)-4(2)+2(5)=5 3-8+10=5 -5+10=5 5=5 true

determine if each is an ordered pair { 4x+y=4 {-2x+2y=-14 (3,-4)

plug (3,-4) into the equations to see if they are an ordered pair 4(3)+(-4)=4 12-4=4 8=4 false -2(3)+2(-4)=-14 -6-8=-14 -14=-14 true one is false so they are not an ordered pair

Solve the system of equations by substitution. {3x + 4y = 32 {3x + y = 17

1). 3x+4y=32 2). y=-3x+17 sub equation 2 into equation 1. 3x+4(-3x+17)=32 3x-12x+68=32 -9x +68=32 -68 -68 -9x=-36 /-9 /-9 x=4 plug x=4 into one equation y=-3(4)+17 y=-12+17 y=5 one solution= (4,5)

solve the system of equations {4x-5y=3 {3x-6y=-9

find one term to get rid of I picked x. times them to make them opposites for x. -3(4x-5y=3) 4(3x-6y=-9) = -12x+15y=-9 12x-24y=-36 add together -9y=-45 /-9 /-9 y=5 plug y=5 into equation 4x-5(5)=3 4x-25=3 +25 +25 4x=22 /4 /4 x=22/4 x=11/2 one solution= (11/2, 5)

solve the system of equations {1/2x+3/4y=-1/4 {3/4x-1/4y=1

first need to find LCD-Least Common Denominator 2 and 4 both can go into 4, LCD=4 times all sides by LCD=4 4(1/2x+3/4y=-1/4) 4(3/4x-1/4y=1) = 4/2x+12/4y=-4/4 12/4x-4/4y=4 = 2x+3y=-1 3x-y=4 now find which want to eliminate or substitue i think substitution is easier on this one so i chose 3x-y=4 to sub into 2x+3y=-1 need 3x-y=4 in y=mx+b form -3x -3x -y=-3x+4 /-1 /-1 y=3x-4 plug into 2x+3y=-1 2x+3(3x-4)=-1 2x+9x-12=-1 11x-12=-1 +12 +12 11x=11 /11 /11 x=1 plug 1 into one of the first equations 2(1)+3y=-1 -2 -2 3y=-3 /3 /3 y=-1 solution= (1,-1)

determine if each is an ordered pair {2x-3y=-9 {-4x+2y=-2 (3,5)

plug (3,5) into the equations to see if they are an ordered pair 2(3)-3(5)=-9 6-15=-9 -9=-9 true -4(3)+2(5)=-2 -12+10=-2 -2=-2 true both are true= they are an ordered pair