Algebra - Simultaneous Equations - Solving by Substitution

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Question 1


Solve the following simultaneous equations by substitution

a) $x=2$
  $y=3x$a s v d
b) $x=5$
  $y=4x$a s v d
c) $x=11$
  $y=10x$a s v d
d) $y=6$
  $x=2y$a s v d
e) $y=7$
  $x=5y$a s v d
f) $y=x+5$
  $x=4$a s v d
g) $x=16$
  $y=2x-1$a s v d
h) $x=4+2y$
  $y=8$a s v d


Question 2


Solve the following simultaneous equations by substitution

a) $y=x+1$
  $y=2x$a s v d
b) $y=x+4$
  $y=2x$a s v d
c) $y=5x$
  $y=x+20$a s v d
d) $y=2x+6$
  $y=4x$a s v d
e) $y=7x$
  $y=3x+40$a s v d
f) $y=7x-6$
  $y=6x$a s v d
g) $y=5x-2$
  $y=3x$a s v d
h) $y=10x-16$
  $y=6x$a s v d


Question 3


Solve the following simultaneous equations by substitution

a) $y=4x+4$
  $y=3x+5$a s v d
b) $y=7x+2$
  $y=6x+10$a s v d
c) $y=5x+3$
  $y=6x+1$a s v d
d) $y=14x+12$
  $y=15x+2$a s v d
e) $y=4x-4$
  $y=3x+3$a s v d
f) $y=7x-1$
  $y=6x+8$a s v d
g) $y=3x+10$
  $y=4x-10$a s v d
h) $x=y+4$
  $x=2y-4$a s v d


Question 4


Solve the following simultaneous equations by substitution

a) $y=x+2$
  $y=2x+1$a s v d
b) $y=x+5$
  $y=3x+1$a s v d
c) $y=x+10$
  $y=2x+6$a s v d
d) $y=x+20$
  $y=4x+2$a s v d
e) $y=3x+4$
  $y=x+14$a s v d
f) $y=6x+10$
  $y=x+60$a s v d
g) $y=8x+5$
  $y=x+68$a s v d
h) $y=x+78$
  $y=12x+1$a s v d


Question 5


Solve the following simultaneous equations by substitution

a) $y=4x+6$
  $y=2x+8$a s v d
b) $y=11x+8$
  $y=8x+20$a s v d
c) $y=11x+22$
  $y=17x+10$a s v d
d) $y=6x+32$
  $y=11x+2$a s v d
e) $y=10x-23$
  $y=3x+5$a s v d
f) $y=2x+6$
  $y=5x-9$a s v d
g) $y=5x-5$
  $y=7x-21$a s v d
h) $x=5-3y$
  $x=7y-5$a s v d


Question 6


Solve the following simultaneous equations by substitution

a) $y=2x+1$
  $x=y-2$a s v d
b) $y=5x+3$
  $x=y-11$a s v d
c) $x=y-6$
  $y=3x-2$a s v d
d) $y=6x-10$
  $x=y-20$a s v d
e) $x=2y-2$
  $y=2x-1$a s v d
f) $y=2x+7$
  $x=37-y$a s v d
g) $y=6x-10$
  $x=13+3y$a s v d
h) $a=11-2b$
  $b=10-2a$a s v d


Question 7


Solve the following simultaneous equations by substitution

a) $2x+3y=13$
  $2x=y+1$a s v d
b) $4x+5y=34$
  $4x=10y+4$a s v d
c) $3x+y=13$
  $y=4x-1$a s v d
d) $5x+4y=9$
  $4y=x-1$a s v d
e) $3x+2y=46$
  $3x=4y-2$a s v d
f) $6y-2x=46$
  $6y=10x+14$a s v d
g) $2x-y=8$
  $2x=y+8$a s v d
h) $3y-2x=-1$
  $2x=2y-2$a s v d


Question 8


Solve the following simultaneous equations by substitution

a) $4x+3y=18$
  $2x=4y-2$a s v d
b) $6x+2y=42$
  $2x=2y-2$a s v d
c) $10x+y=104$
  $5x=10y+10$a s v d
d) $12x+4y=44$
  $3x=2y-4$a s v d
e) $6x+y=46$
  $4x=2y+4$a s v d
f) $10x+5y=5$
  $6x=3y+9$a s v d
g) $5x+2y=-5$
  $3x=3y-24$a s v d
h) $7x-5y=8$
  $5x=10y+70$a s v d


Question 9


Solve the following simultaneous equations by substitution

a) $2x+3x=24$
  $2x-y=1$a s v d
b) $8x+3y=58$
  $4y-3x=9$a s v d
c) $3x+7y=38$
  $3x+2y=28$a s v d
d) $5x+6y=27$
  $3x+6y=21$a s v d
e) $6x+5y=63$
  $3x-2y=18$a s v d
f) $2x+10y=92$
  $3x+5y=48$a s v d
g) $2x+9y=51$
  $6x+2y=28$a s v d
h) $2x+5y=41$
  $3x+7y=59$a s v d


Question 10


Solve the following simultaneous equations by substitution

a) $4x+9y=19$
  $5x+10y=20$a s v d
b) $2x-3y=4$
  $4x-8y=12$a s v d
c) $3x-2y=31$
  $5x+3y=20$a s v d
d) $5y-2x=6$
  $3x+2y=-28$a s v d
e) $x+y=0$
  $4x-4y=40$a s v d
f) $3x-5y=21$
  $7x-9y=57$a s v d
g) $17y-10x=-180$
  $4x+5x=-46$a s v d
h) $7x+13y=-192$
  $5y-11x=86$a s v d


Question 11


Solve the following simultaneous equations by substitution. Express your answers as top-heavy/improper fractions where necessary

a) $5x+4y=17$
  $3x-2y=8$a s v d
b) $6x+5y=32$
  $18x-y=0$a s v d
c) $8x+3y=4$
  $8x-15y=-8$a s v d
d) $10x-y=7$
  $5x-y=4$a s v d
e) $6x+2y=16$
  $3x-y=7$a s v d
f) $4x-y=6$
  $3x-3y=6$a s v d
g) $3x+4y=\frac{99}{20}$
  $4x+3y=\frac{41}{10}$a s v d
h) $5x-2y=-\frac{51}{7}$
  $3x+5y=\frac{69}{14}$a s v d