Algebra - Solving Simultaneous Equations Graphically Questions
Question 1
Find the point of intersection for the following graphs
a)
a
$(2,4)$
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b)
a
$(1,4)$
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c)
a
$(2,1)$
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d)
a
$(3,-1)$
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Question 2
Find the solution to the following pair of equations. Use the graphs to find this.
a) $y=x-3$ and $y=-x+5$
a
$x=4,y=1$
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b) $y=5x+2$ and $y=x+6$
a
$x=1,y=7$
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c) $y=2x+6$ and $y=\frac12x+3$
a
$x=-2,y=2$
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d) $2x+3y=0$ and $x+y=2$
a
$x=6,y=-4$
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Question 3
Use the given graphs to solve the following equations

a) $y=x$ and $y=4x+6$
a
$x=-2,y=-2$
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b) $y=x$ and $y=-2x+6$
a
$x=2,y=2$
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c) $y=4x+6$ and $y=-2x+6$
a
$x=0,y=6$
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Question 4
Solve these simultaneous equations graphically
a) $y=2x$ and $y=x+1$
a
$x=1,y=2$
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b) $y=2x-2$ and $y=\frac12x+1$
a
$x=2,y=2$
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c) $y=-x+3$ and $y=4x+8$
a
$x=-1,y=4$
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d) $y=-2x+5$ and $y=-x-1$
a
$x=6,y=-7$
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Question 5
Answer the following
a) Graph $y=2x+6$ and $x-\frac12y=0$ on the same number plane
a
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b) Will solutions be obtained if the equations $y=2x+6$ and $x-\frac12y=0$ are solved simultaneously? Why?
a
No, as they are parallel lines so never intersect, therefore there is no value of $x$ and $y$ that satifies both equations at the same time.
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Question 6
Solve these simultaneous equations graphically
a) $x+y=0$ and $y=x+2$
a
$x=-1,y=1$
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b) $x+3y=6$ and $2x-y+2=0$
a
$x=0,y=2$
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c) $4x-y-7=0$ and $3x+4y-10=0$
a
$x=2,y=1$
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d) $2x+5y-9=0$ and $5x+9y-12=0$
a
$x=-3,y=3$
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Question 7
Solve these simultaneous equations graphically. Round your answers to $1$ decimal place.
a) $y=-5x-2$ and $y=\frac13x+4$
a
$x=-1.1,y=3.6$
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b) $2x-5y-1=0$ and $3x+y=-4$
a
$x=-1.1,y=-0.6$
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Question 1
Find the point of intersection for the following graphs
a)

b)

c)

d)

Question 2
Find the solution to the following pair of equations. Use the graphs to find this.
a) $y=x-3$ and $y=-x+5$

b) $y=5x+2$ and $y=x+6$

c) $y=2x+6$ and $y=\frac12x+3$

d) $2x+3y=0$ and $x+y=2$

Question 3
Use the given graphs to solve the following equations

a) $y=x$ and $y=4x+6$
b) $y=x$ and $y=-2x+6$
c) $y=4x+6$ and $y=-2x+6$
Question 4
Solve these simultaneous equations graphically
a) $y=2x$ and $y=x+1$
b) $y=2x-2$ and $y=\frac12x+1$
c) $y=-x+3$ and $y=4x+8$
d) $y=-2x+5$ and $y=-x-1$
Question 5
Answer the following
a) Graph $y=2x+6$ and $x-\frac12y=0$ on the same number plane
b) Will solutions be obtained if the equations $y=2x+6$ and $x-\frac12y=0$ are solved simultaneously? Why?
Question 6
Solve these simultaneous equations graphically
a) $x+y=0$ and $y=x+2$
b) $x+3y=6$ and $2x-y+2=0$
c) $4x-y-7=0$ and $3x+4y-10=0$
d) $2x+5y-9=0$ and $5x+9y-12=0$
Question 7
Solve these simultaneous equations graphically. Round your answers to $1$ decimal place.
a) $y=-5x-2$ and $y=\frac13x+4$
b) $2x-5y-1=0$ and $3x+y=-4$
Answers
Question 1
a) $(2,4)$
b) $(1,4)$
c) $(2,1)$
d) $(3,-1)$
Question 2
a) $x=4,y=1$
b) $x=1,y=7$
c) $x=-2,y=2$
d) $x=6,y=-4$
Question 3
a) $x=-2,y=-2$
b) $x=2,y=2$
c) $x=0,y=6$
Question 4
a) $x=1,y=2$

b) $x=2,y=2$

c) $x=-1,y=4$

d) $x=6,y=-7$

Question 5
a)

b) No, as they are parallel lines so never intersect, therefore there is no value of $x$ and $y$ that satifies both equations at the same time.
Question 6
a) $x=-1,y=1$

b) $x=0,y=2$

c) $x=2,y=1$

d) $x=-3,y=3$

Question 7
a) $x=-1.1,y=3.6$

b) $x=-1.1,y=-0.6$

Question 1
Find the point of intersection for the following graphs
a)

b)

c)

d)

Question 2
Find the solution to the following pair of equations. Use the graphs to find this.
a) $y=x-3$ and $y=-x+5$

b) $y=5x+2$ and $y=x+6$

c) $y=2x+6$ and $y=\frac12x+3$

d) $2x+3y=0$ and $x+y=2$

Question 3
Use the given graphs to solve the following equations

a) $y=x$ and $y=4x+6$
b) $y=x$ and $y=-2x+6$
c) $y=4x+6$ and $y=-2x+6$
Question 4
Solve these simultaneous equations graphically
a) $y=2x$ and $y=x+1$
b) $y=2x-2$ and $y=\frac12x+1$
c) $y=-x+3$ and $y=4x+8$
d) $y=-2x+5$ and $y=-x-1$
Question 5
Answer the following
a) Graph $y=2x+6$ and $x-\frac12y=0$ on the same number plane
b) Will solutions be obtained if the equations $y=2x+6$ and $x-\frac12y=0$ are solved simultaneously? Why?
Question 6
Solve these simultaneous equations graphically
a) $x+y=0$ and $y=x+2$
b) $x+3y=6$ and $2x-y+2=0$
c) $4x-y-7=0$ and $3x+4y-10=0$
d) $2x+5y-9=0$ and $5x+9y-12=0$
Question 7
Solve these simultaneous equations graphically. Round your answers to $1$ decimal place.
a) $y=-5x-2$ and $y=\frac13x+4$
b) $2x-5y-1=0$ and $3x+y=-4$
Answers
Question 1
a) $(2,4)$
b) $(1,4)$
c) $(2,1)$
d) $(3,-1)$
Question 2
a) $x=4,y=1$
b) $x=1,y=7$
c) $x=-2,y=2$
d) $x=6,y=-4$
Question 3
a) $x=-2,y=-2$
b) $x=2,y=2$
c) $x=0,y=6$
Question 4
a) $x=1,y=2$

b) $x=2,y=2$

c) $x=-1,y=4$

d) $x=6,y=-7$

Question 5
a)

b) No, as they are parallel lines so never intersect, therefore there is no value of $x$ and $y$ that satifies both equations at the same time.
Question 6
a) $x=-1,y=1$

b) $x=0,y=2$

c) $x=2,y=1$

d) $x=-3,y=3$

Question 7
a) $x=-1.1,y=3.6$

b) $x=-1.1,y=-0.6$

Solutions
Question 1
a)
b)
c)
d)
Question 2
a)
b)
c)
d)
Question 3
a)
b)
c)
Question 4
a)
b)
c)
d)
Question 5
a)
b)
Question 6
a)
b)
c)
d)
Question 7
a)
b)