Algebra - Simultaneous Equations - Solving by Any Method

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Question 1

Solve the following simultaneous equations

a) $\begin{align}y&=x+2\\y&=2x+1\end{align}$ a

$x=1$, $y=3$

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b) $\begin{align}x+y&=5\\x-y&=1\end{align}$ a

$x=3$, $y=2$

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c) $\begin{align}x&=2y+8\\x&=3y+2\end{align}$ a

$x=20$, $y=6$

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d) $\begin{align}x-3y&=2\\x+3y&=8\end{align}$ a

$x=5$, $y=1$

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e) $\begin{align}x-2y&=3\\x-3y&=0\end{align}$ a

$x=9$, $y=3$

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f) $\begin{align}2y-x&=8\\6y-x&=28\end{align}$ a

$x=2$, $y=5$

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Question 2

Solve the following simultaneous equations

a) $\begin{align}3x+2y&=23\\7x+4y&=51\end{align}$ a

$x=5$, $y=4$

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b) $\begin{align}2y&=6x+4\\y&=5x-4\end{align}$ a

$x=3$, $y=11$

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c) $\begin{align}10y-30&=2x\\4y+2x&=54\end{align}$ a

$x=15$, $y=6$

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d) $\begin{align}3x-5y&=8\\2y+5x&=34\end{align}$ a

$x=6$, $y=2$

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e) $\begin{align}3x&=38-y\\3y&=16-x\end{align}$ a

$x=11$, $y=5$

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f) $\begin{align}7x-3y&=55\\4y&=50-2x\end{align}$ a

$x=5$, $y=10$

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Question 3

Solve the following simultaneous equations

a) $\begin{align}y-2x&=9\\5y&=23-2x\end{align}$ a

$x=-2$, $y=5$

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b) $\begin{align}3y&=4x+3\\2y&=x-2\end{align}$ a

$x=-4$, $y=-3$

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c) $\begin{align}7y&=1+3x\\y+6x&=-32\end{align}$ a

$x=-5$, $y=-2$

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d) $\begin{align}5x-6y&=1\\10x+y&=-11\end{align}$ a

$x=-1$, $y=-1$

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e) $\begin{align}2x-3y&=-1\\3x+2y&=-21\end{align}$ a

$x=-5$, $y=-3$

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f) $\begin{align}4x+7y&=55\\x&=-16-2y\end{align}$ a

$x=-2$, $y=9$

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Question 4

Solve the following simultaneous equations. Leave answers as improper fractions where necessary.

a) $\begin{align}6x&=y+1\\6y&=24x\end{align}$ a

$x=\frac12$, $y=2$

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b) $\begin{align}6x-5y&=1\\9x+10y&=5\end{align}$ a

$x=\frac13$, $y=\frac15$

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c) $\begin{align}12x&=15y+3\\x-y&=\frac{7}{20}\end{align}$ a

$x=\frac34$, $y=-\frac{2}{5}$

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d) $\begin{align}3y&=2x+3\\4y&=5x-1\end{align}$ a

$x=\frac{15}{7}$, $y=\frac{17}{7}$

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e) $\begin{align}5x-2y&=6\\3y&=8x+15\end{align}$ a

$x=-123$, $y=-48$

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f) $\begin{align}3x+10y&=18\\10y-3x&=0\end{align}$ a

$x=3$, $y=\frac{9}{10}$

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Question 1

Solve the following simultaneous equations

a) $\begin{align}y&=x+2\\y&=2x+1\end{align}$

b) $\begin{align}x+y&=5\\x-y&=1\end{align}$

c) $\begin{align}x&=2y+8\\x&=3y+2\end{align}$

d) $\begin{align}x-3y&=2\\x+3y&=8\end{align}$

e) $\begin{align}x-2y&=3\\x-3y&=0\end{align}$

f) $\begin{align}2y-x&=8\\6y-x&=28\end{align}$

Question 2

Solve the following simultaneous equations

a) $\begin{align}3x+2y&=23\\7x+4y&=51\end{align}$

b) $\begin{align}2y&=6x+4\\y&=5x-4\end{align}$

c) $\begin{align}10y-30&=2x\\4y+2x&=54\end{align}$

d) $\begin{align}3x-5y&=8\\2y+5x&=34\end{align}$

e) $\begin{align}3x&=38-y\\3y&=16-x\end{align}$

f) $\begin{align}7x-3y&=55\\4y&=50-2x\end{align}$

Question 3

Solve the following simultaneous equations

a) $\begin{align}y-2x&=9\\5y&=23-2x\end{align}$

b) $\begin{align}3y&=4x+3\\2y&=x-2\end{align}$

c) $\begin{align}7y&=1+3x\\y+6x&=-32\end{align}$

d) $\begin{align}5x-6y&=1\\10x+y&=-11\end{align}$

e) $\begin{align}2x-3y&=-1\\3x+2y&=-21\end{align}$

f) $\begin{align}4x+7y&=55\\x&=-16-2y\end{align}$

Question 4

Solve the following simultaneous equations. Leave answers as improper fractions where necessary.

a) $\begin{align}6x&=y+1\\6y&=24x\end{align}$

b) $\begin{align}6x-5y&=1\\9x+10y&=5\end{align}$

c) $\begin{align}12x&=15y+3\\x-y&=\frac{7}{20}\end{align}$

d) $\begin{align}3y&=2x+3\\4y&=5x-1\end{align}$

e) $\begin{align}5x-2y&=6\\3y&=8x+15\end{align}$

f) $\begin{align}3x+10y&=18\\10y-3x&=0\end{align}$

Answers

Question 1

a) $x=1$, $y=3$

b) $x=3$, $y=2$

c) $x=20$, $y=6$

d) $x=5$, $y=1$

e) $x=9$, $y=3$

f) $x=2$, $y=5$

Question 2

a) $x=5$, $y=4$

b) $x=3$, $y=11$

c) $x=15$, $y=6$

d) $x=6$, $y=2$

e) $x=11$, $y=5$

f) $x=5$, $y=10$

Question 3

a) $x=-2$, $y=5$

b) $x=-4$, $y=-3$

c) $x=-5$, $y=-2$

d) $x=-1$, $y=-1$

e) $x=-5$, $y=-3$

f) $x=-2$, $y=9$

Question 4

a) $x=\frac12$, $y=2$

b) $x=\frac13$, $y=\frac15$

c) $x=\frac34$, $y=-\frac{2}{5}$

d) $x=\frac{15}{7}$, $y=\frac{17}{7}$

e) $x=-123$, $y=-48$

f) $x=3$, $y=\frac{9}{10}$

Question 1

Solve the following simultaneous equations

a) $\begin{align}y&=x+2\\y&=2x+1\end{align}$

b) $\begin{align}x+y&=5\\x-y&=1\end{align}$

c) $\begin{align}x&=2y+8\\x&=3y+2\end{align}$

d) $\begin{align}x-3y&=2\\x+3y&=8\end{align}$

e) $\begin{align}x-2y&=3\\x-3y&=0\end{align}$

f) $\begin{align}2y-x&=8\\6y-x&=28\end{align}$

Question 2

Solve the following simultaneous equations

a) $\begin{align}3x+2y&=23\\7x+4y&=51\end{align}$

b) $\begin{align}2y&=6x+4\\y&=5x-4\end{align}$

c) $\begin{align}10y-30&=2x\\4y+2x&=54\end{align}$

d) $\begin{align}3x-5y&=8\\2y+5x&=34\end{align}$

e) $\begin{align}3x&=38-y\\3y&=16-x\end{align}$

f) $\begin{align}7x-3y&=55\\4y&=50-2x\end{align}$

Question 3

Solve the following simultaneous equations

a) $\begin{align}y-2x&=9\\5y&=23-2x\end{align}$

b) $\begin{align}3y&=4x+3\\2y&=x-2\end{align}$

c) $\begin{align}7y&=1+3x\\y+6x&=-32\end{align}$

d) $\begin{align}5x-6y&=1\\10x+y&=-11\end{align}$

e) $\begin{align}2x-3y&=-1\\3x+2y&=-21\end{align}$

f) $\begin{align}4x+7y&=55\\x&=-16-2y\end{align}$

Question 4

Solve the following simultaneous equations. Leave answers as improper fractions where necessary.

a) $\begin{align}6x&=y+1\\6y&=24x\end{align}$

b) $\begin{align}6x-5y&=1\\9x+10y&=5\end{align}$

c) $\begin{align}12x&=15y+3\\x-y&=\frac{7}{20}\end{align}$

d) $\begin{align}3y&=2x+3\\4y&=5x-1\end{align}$

e) $\begin{align}5x-2y&=6\\3y&=8x+15\end{align}$

f) $\begin{align}3x+10y&=18\\10y-3x&=0\end{align}$

Answers

Question 1

a) $x=1$, $y=3$
b) $x=3$, $y=2$
c) $x=20$, $y=6$
d) $x=5$, $y=1$
e) $x=9$, $y=3$
f) $x=2$, $y=5$

Question 2

a) $x=5$, $y=4$
b) $x=3$, $y=11$
c) $x=15$, $y=6$
d) $x=6$, $y=2$
e) $x=11$, $y=5$
f) $x=5$, $y=10$

Question 3

a) $x=-2$, $y=5$
b) $x=-4$, $y=-3$
c) $x=-5$, $y=-2$
d) $x=-1$, $y=-1$
e) $x=-5$, $y=-3$
f) $x=-2$, $y=9$

Question 4

a) $x=\frac12$, $y=2$
b) $x=\frac13$, $y=\frac15$
c) $x=\frac34$, $y=-\frac{2}{5}$
d) $x=\frac{15}{7}$, $y=\frac{17}{7}$
e) $x=-123$, $y=-48$
f) $x=3$, $y=\frac{9}{10}$

Algebra - Simultaneous Equations - Solving by Any Method

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