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Algebra - Simultaneous Equations - Solving by Elimination

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Question 1


Solve the following simulatenous equations by elimination

a) $x+y=5$
  $x=2$  a s v d
b) $x+y=18$
  $x=13$  a s v d
c) $x+y=7$
  $y=4$  a s v d
d) $x+y=14$
  $y=6$  a s v d
e) $x+2y=6$
  $x=2$  a s v d
f) $x+5y=9$
  $x=4$  a s v d
g) $2x+y=17$
  $y=3$  a s v d
h) $8x+y=30$
  $y=6$  a s v d


Question 2


Solve the following simulatenous equations by elimination

a) $2x+3y=8$
  $2x=2$  a s v d
b) $3x+5y=27$
  $3x=12$  a s v d
c) $7x+4y=27$
  $4y=20$  a s v d
d) $2x+5y=30$
  $5y=10$  a s v d
e) $2x+3y=33$
  $x=3$  a s v d
f) $3x+9y=24$
  $x=5$  a s v d
g) $8x+5y=26$
  $y=2$  a s v d
h) $5x+7y=67$
  $y=6$  a s v d


Question 3


Solve the following simulatenous equations by elimination

a) $x-y=7$
  $y=2$  a s v d
b) $x-y=15$
  $y=5$  a s v d
c) $y-x=100$
  $x=16$  a s v d
d) $x-2y=5$
  $2y=8$  a s v d
e) $10x-6y=2$
  $6y=18$  a s v d
f) $3x-2y=22$
  $y=1$  a s v d
g) $9x-5y=12$
  $y=3$  a s v d
h) $7x-8y=6$
  $y=8$  a s v d


Question 4


Solve the following simulatenous equations by elimination

a) $x+y=7$
  $x-y=1$  a s v d
b) $x+y=9$
  $x-y=5$  a s v d
c) $2x+y=13$
  $x-y=2$  a s v d
d) $3x+y=31$
  $x-y=9$  a s v d
e) $2x+y=12$
  $2x-y=8$  a s v d
f) $2x+y=13$
  $3x-y=7$  a s v d
g) $6x+2y=30$
  $5x-2y=3$  a s v d
h) $x+5y=44$
  $8x-5y=37$  a s v d


Question 5


Solve the following simulatenous equations by elimination

a) $2x+y=13$
  $x+y=8$  a s v d
b) $3x+y=15$
  $2x+y=12$  a s v d
c) $7x+y=15$
  $6x+y=13$  a s v d
d) $3x+y=10$
  $x+y=8$  a s v d
e) $7x+y=65$
  $4x+y=38$  a s v d
f) $x+5y=29$
  $x+2y=14$  a s v d
g) $x+10y=46$
  $x+3y=18$  a s v d
h) $3x+6y=69$
  $3x+y=29$  a s v d


Question 6


Solve the following simulatenous equations by elimination

a) $3x-y=12$
  $5x+y=28$  a s v d
b) $x+5y=17$
  $x+y=9$  a s v d
c) $x+6y=16$
  $x-2y=8$  a s v d
d) $3x-y=2$
  $4x-y=4$  a s v d
e) $3x-3y=27$
  $x-3y=3$  a s v d
f) $4x-3y=21$
  $4x+8y=76$  a s v d
g) $x+2y=5$
  $5x-2y=-11$  a s v d
h) $6x+3y=-9$
  $-6x-5y=17$  a s v d


Question 7


Solve the following simulatenous equations by elimination

a) $2x+3y=19$
  $x+y=7$  a s v d
b) $x+3y=6$
  $5x+y=16$  a s v d
c) $2x+2y=26$
  $5x+y=33$  a s v d
d) $3x+5y=14$
  $x+7y=10$  a s v d
e) $4x+3y=23$
  $2x+5y=29$  a s v d
f) $3x+6y=15$
  $4x+2y=14$  a s v d
g) $10x+2y=78$
  $5x+7y=93$  a s v d
h) $8x+4y=52$
  $9x+12y=96$  a s v d


Question 8


Solve the following simulatenous equations by elimination

a) $3x-y=5$
  $4x+2y=10$  a s v d
b) $4x-y=17$
  $5x+3y=34$  a s v d
c) $x+5y=37$
  $-2x+2y=10$  a s v d
d) $x+8y=81$
  $-5x+9y=85$  a s v d
e) $3x-2y=18$
  $5x+4y=52$  a s v d
f) $3x-3y=24$
  $2x+9y=38$  a s v d
g) $-2x-3y=-37$
  $6x+8y=102$  a s v d
h) $20x-5y=35$
  $-4x+7y=23$  a s v d


Question 9


Solve the following simulatenous equations by elimination

a) $2x+3y=8$
  $3x+7y=17$  a s v d
b) $5x+2y=31$
  $4x+3y=29$  a s v d
c) $8x-4y=4$
  $10x+5y=75$  a s v d
d) $-2x-3y=-12$
  $3x+7y=23$  a s v d
e) $4x+5y=39$
  $3x+3y=27$  a s v d
f) $4x-3y=29$
  $3x+4y=53$  a s v d
g) $5x+7y=78$
  $3x+2y=27$  a s v d
h) $10x+9y=162$
  $6x-5y=14$  a s v d


Question 10


Solve the following simulatenous equations by elimination. Answers may be negative numbers

a) $3x+4y=5$
  $2x+5y=8$  a s v d
b) $5x+3y=9$
  $2x-4y=14$  a s v d
c) $7x-2y=-8$
  $3x-5y=9$  a s v d
d) $2x-3y=21$
  $5x-2y=25$  a s v d
e) $-2x-5y=32$
  $3x-4y=-2$  a s v d
f) $-3x+8y=30$
  $7x-3y=-70$  a s v d
g) $5x+2y=12$
  $8x+9y=-4$  a s v d
h) $11x+2y=-123$
  $2x-11y=114$  a s v d


Question 11


Solve the following simulatenous equations by elimination. Answers may be fractions or negative. Leave fractions as improper/top heavy fractions where necessary

a) $4x+2y=6$
  $6x+4y=11$  a s v d
b) $3x-3y=14$
  $2x+12y=14$  a s v d
c) $6x-4y=3$
  $15x-16y=6$  a s v d
d) $5x+2y=6$
  $8x-3y=\frac{3}{10}$  a s v d
e) $2x-3y=-4$
  $5x-2y=-5\frac{5}{12}6$  a s v d
f) $16x+40y=-2$
  $2x-15y=-\frac54$  a s v d
g) $3x-4y=\frac{29}{5}$
  $16x+9y=-44\frac{9}{10}$  a s v d
h) $\frac12x+3y=-1\frac{182}{187}$
  $\frac25x-2\frac34y=-\frac{239}{3740}$  a s v d