# 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
$x=2,y=1$

Question ID: 20320050030

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d) $2x+5y-9=0$ and $5x+9y-12=0$

a
$x=-3,y=3$

Question ID: 20320050040

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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
$x=-1.1,y=3.6$

Question ID: 20320060010

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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)