# 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