Answer:
1. (-3,8) 2.(-10,1) 3.(8,2) 4.(2,5) 5.(0,4) 6.(1,1) 7.(-8,-5)
Step-by-step explanation:
Question number 1:
Step: Solvey=5x+23for y:
Step: Substitute 5x+23 for y in3x+2y=7:
3x+2y=7
3x+2(5x+23)=7
13x+46=7(Simplify both sides of the equation)
13x+46+−46=7+−46(Add -46 to both sides)
13x=−39
[tex]\frac{3x}{3} =\frac{-39}{3}[/tex] Divide by both sides by -3
x=-3
Substitute−3forxiny=5x+23
y=5x+23
y=(5)(−3)+23
y=8
Question number 2:
Solve x=−10for x
Substitute−10 for x in x+3y=−7
x+3y=−7
-10+3y=-7
3y−10=−7
3y−10+10=−7+10 Add 10 to both sides
3y=3
[tex]\frac{3y}{3} =\frac{3}{3}[/tex]
y=1
Question number 3:
Solve−2x+18=2for x
−2x+18+−18=2+−18 Add -18 to both sides
−2x=−16
[tex]\frac{-2x}{-2} =\frac{-16}{-2}[/tex] Divide both sides by -2
x=8
Substitute 8 for x in x=6y−4
x=6y−4
8=6y−4
8+−6y=6y−4+−6y Add -6y to both sides
−6y+8=−4
−6y+8+−8=−4+−8 Add -8 to both sides
−6y=−12
[tex]\frac{-6y}{-6} =\frac{-12}{-6}[/tex]
y=2
Question number 4:
Solve y=2x+1 for y
Substitute 2x+1 for y in y=−7x+19
y=−7x+19
2x+1=−7x+19
2x+1+7x=−7x+19+7x Add 7x to both sides
9x+1=19
9x+1+−1=19+−1 Add -1 to both sides
9x=18
[tex]\frac{9x}{9} =\frac{18}{9}[/tex] Divide both sides by 9
x=2
Substitute2 for x in y=2x+1
y=2x+1
y=(2)(2)+1
y=5
Question number 5:
Solvey=−10x+4for y:
Step: Substitute−10x+4foryinx−3y=−12:
x−3y=−12
x−3(−10x+4)=−12
31x−12=−12
31x−12+12=−12+12 Add 12 to both sides
31x=0
[tex]\frac{31x}{31} =\frac{0}{31}[/tex] Divide both sides by 31
x=0
Substitute0forxiny=−10x+4:
y=−10x+4
y=(−10)(0)+4
y=4
Question number 6:
Solvex=yfor x:
Step: Substitute y for x in 3x+7y=10:
3x+7y=10
3y+7y=10 Combine like terms
10y=10
[tex]\frac{10y}{10} =\frac{10}{10}[/tex] Divide both sides by 10
y=1
Substitute 1 for y in x=y:
x=y
x=1
Question number 7:
Solvex=−y−13for x:
Step: Substitute−y−13forxin−2x−y=21:
−2x−y=21
−2(−y−13)−y=21
y+26=21
y+26+−26=21+−26 Add -26 to both sides
y=-5
Substitute−5foryinx=−y−13:
x=−y−13
x=−(−5)−13
x=−8
