Algebraic Solution: Solve using the substitution method

Examples with solutions for Algebraic Solution: Solve using the substitution method

Exercise #1

Solve the following equations:

(I)2x+y=9 (I)2x+y=9

(II)x=5 (II)x=5

Video Solution

Answer

x=5,y=1 x=5,y=-1

Exercise #2

Solve the following equations:

(I)x+y=18 (I)x+y=18

(II)y=13 (II)y=13

Video Solution

Answer

x=5,y=13 x=5,y=13

Exercise #3

Find the value of x and and band the substitution method.

(I)x2and=4 (I)-x-2and=4

(II)3x+and=8 (II)3x+and=8

Video Solution

Answer

x=4,y=4 x=4,y=-4

Exercise #4

Find the value of x and and band the substitution method.

(I)x+and=5 (I)x+and=5

(II)2x3and=15 (II)2x-3and=-15

Video Solution

Answer

x=0,y=5 x=0,y=5

Exercise #5

Find the value of x and and band the substitution method.

(I)5x+9and=18 (I)-5x+9and=18

(II)x+8and=16 (II)x+8and=16

Video Solution

Answer

x=0,y=2 x=0,y=2

Exercise #6

Find the value of x and and band the substitution method.

(I)x+3and=12 (I)-x+3and=12

(II)4x+2and=10 (II)4x+2and=10

Video Solution

Answer

x=37,y=297 x=\frac{3}{7},y=\frac{29}{7}

Exercise #7

Choose the correct answer for the following exercise:

(I)x+y=15 (I)x+y=15

(II)2x+2y=12 (II)2x+2y=12\frac{}{}

Video Solution

Answer

No solution

Exercise #8

Find the value of x and and band the substitution method.

(I)5x+and=8 (I)-5x+and=8

(II)3x2and=11 (II)3x-2and=11

Video Solution

Answer

x=277,y=797 x=-\frac{27}{7},y=-\frac{79}{7}

Exercise #9

Find the value of x and and band the substitution method.

(I)4x+4and=15 (I)-4x+4and=15

(II)2x+8and=12 (II)2x+8and=12

Video Solution

Answer

x=95,y=3920 x=-\frac{9}{5},y=\frac{39}{20}

Exercise #10

Choose the correct answer for the following exercise:

(I)2x+3y=14 (I)-2x+3y=14

(II)4x+6y=28 (II)-4x+6y=28

Video Solution

Answer

Infinite solutions

Exercise #11

Find the value of x and and band the substitution method.

(I)x+4and=53and (I)x+4and=5-3and

(II)2x+3and=6 (II)2x+3and=6

Video Solution

Answer

x=2711,y=411 x=\frac{27}{11},y=\frac{4}{11}

Exercise #12

Find the value of x and and band the substitution method.

(I)8x2and=10 (I)8x-2and=10

(II)3x+3and=9 (II)3x+3and=9

Video Solution

Answer

x=85,y=1410 x=\frac{8}{5},y=\frac{14}{10}

Exercise #13

Choose the correct answer for the following exercise:

(I)8x+5y=10 (I)-8x+5y=10

(II)24x+15y=30 (II)-24x+15y=30

Video Solution

Answer

Infinite solutions

Exercise #14

Choose the correct answer for the following exercise:

(I)3x4y=10 (I)3x-4y=10

(II)9x12y=15 (II)9x-12y=15

Video Solution

Answer

No solution

Exercise #15

Solve the following equations for x and y using the substitution method:

(I)2xy2+3y+x5=7 (I)\frac{2x-y}{2}+\frac{-3y+x}{5}=7

(II)yx85y+x6=4 (II)\frac{-y-x}{8}-\frac{5y+x}{6}=4

Video Solution

Answer

x=1.57,y=4.65 x=1.57,y=-4.65

Exercise #16

Look at the two equations below. Calculate the values of x and y using the substitution method.

{xy2+y+x3=6yx5y+x1=8 \begin{cases}\frac{x-y}{2}+\frac{-y+x}{3}=-6 \\ \frac{-y-x}{5}-\frac{y+x}{1}=8\end{cases}

Video Solution

Answer

x=6.933,y=0.266 x=-6.933,y=0.266

Exercise #17

Choose the correct answer for the following exercise:

(I)8x+5y=2 (I)-8x+5y=2

(II)16x+10y=5 (II)-16x+10y=5

Video Solution

Answer

No solution

Exercise #18

Solve the following equations for x and y using the substitution method:

(I)2x3y4+xy5=30 (I)\frac{2x-3y}{4}+\frac{x-y}{5}=30

(II)2y+x83yx4=12 (II)\frac{2y+x}{8}-\frac{3y-x}{4}=12

Video Solution

Answer

x=576,y=456 x=-576,y=-456

Exercise #19

Solve the following equations for x and y using the substitution method.

(I)3x2y8+xy2=14 (I)\frac{3x-2y}{8}+\frac{x-y}{2}=14

(II)4x+3y52x2y3=20 (II)\frac{4x+3y}{5}-\frac{2x-2y}{3}=20

Video Solution

Answer

x=27.08,y=12.93 x=27.08,y=12.93

Exercise #20

Solve the following equations for x and y using the substitution method.

(I)x+3y6+5xy3=12 (I)\frac{-x+3y}{6}+\frac{5x-y}{3}=12

(II)2x4y102x2y5=15 (II)\frac{2x-4y}{10}-\frac{-2x-2y}{5}=15

Video Solution

Answer

x=25,y=153 x=25,y=-153