Solving Simultaneous Equations - Questions - Class Mathematics School Portal

Solving Simultaneous Equations - Questions

Question 1

15729

The solutions to the simultaneous equations

$7x - 5y = 16$

$2x + 7y = 13$ are?

Answer

$x=3$, $y=1$

Worked Solution

Question 2

15730

The solutions to the simultaneous equations

$x + y = 9$

${x^2} + xy + {y^2} = 61$ are?

Answer

$x=5,y=4$

$x=4,y=5$

Worked Solution

Question 3

15590

${\rm{5}}$ pencils and ${\rm{4}}$ erasers can be purchased for ${\rm{\$ 1}}{\rm{.}}$ At the same shop, I can buy ${\rm{15}}$ pencils and ${\rm{2 }}$ erasers for ${\rm{\$ 2}}{\rm{.}}$ What is the price of a pencil, in cents?

Answer

$12\,{\rm{cents}}$

Worked Solution

Question 4

15586

A large pizza is priced ${\rm{25\% }}$ more than a medium size pizza. The Walker family ordered ${\rm{5}}$ medium pizzas and ${\rm{8 }}$ large pizzas for ${\rm{\$ 120}}{\rm{. }}$ The Johnson's ordered ${\rm{10}}$ medium pizzas with ${\rm{12}}$ large pizzas. What was the Johnson's total bill?

Answer

$\$ 200$

Worked Solution

Question 5

15580

Solve the following simultaneous equations using elimination method

$2x + 3y = 10$

$5x - 3y = 4$

Answer

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

Worked Solution

Question 6

15578

Solve the following simultaneous equations using elimination method

$x - y + 3 = 0$

$11x - 6y - 2 = 0$

Answer

$x = 4,\,\,\,y = 7$

Worked Solution

Question 7

15571

Solve the following simultaneous equations using substitution method

$x + 15y = 20$

$3x - 8y = 7$

Answer

$x = 5,\,\,\,y = 1$

Worked Solution

Question 8

13196

The solutions to $y = x - 3$ and $2x + 3y = 26$ are?

Answer

$x = 7,\,y = 4$

Worked Solution

Question 9

13197

The solutions to $2x + y=8$ and $x - 3y = 11$ are?

Answer

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

Worked Solution

Question 10

13198

The larger of two numbers is three times the smaller and their difference is 34. The numbers are?

Answer

$51,\,17$

Worked Solution

Question 11

13199

A rectangle has a perimeter of 56cm. If 4cm is taken from the length and added to the width the rectangle becomes a square. The dimensions of the original rectangle are?

Answer

$l = 18,\,w = 10$

Worked Solution

Question 12

13200

The solutions to $x - y= 1$ and $xy = 2$ are?

Answer

$x = - 1,\,y = - 2{\text{ or }}x = 2,\,y = 1$

Worked Solution

Question 13

25858

Solve the simultaneous equations

\[\begin{array}{*{20}{c}}{y = 4x + 8}\\{y = 4 - {x^2}}\end{array}\]

Answer

$x=-2$, $y=0$

Worked Solution

Question 14

21373

Solve simultaneously $\begin{array}{l}y = x - 3\\2x + 3y = 26\end{array}$

Answer

$x=7$, $y=4$

Worked Solution

Question 15

34994

Solve simultaneously: $\begin{array}{*{20}{c}}{y = x - 3}\\{xy = 10}\end{array}$

Answer

$\left( {5,2} \right)$ and $\left( {-2,-5} \right)$

Worked Solution

Question 16

34995

Solve simultaneously: $\begin{array}{*{20}{c}}{y-2x=1}\\{x^2+y^2=10}\end{array}$

Answer

$\rm{(1,3)}$ and $\rm{ (\dfrac{-9}{5},\dfrac{-13}{5})}$

Worked Solution

Question 17

28615

Find the points of intersection of the line $y = 5x + 6$ and the parabola $y = {x^2}.$

Answer

$\left( {6,36} \right)$ and $\left( { - 1,1} \right)$

Worked Solution

Question 18

28617

Solve simultaneous $\begin{array}{*{20}{c}}{y = 2x - 5}\\{y = {x^2} - 4x + 4}\end{array}$

Answer

$(3,1)$

Worked Solution

Question 19

28616

Find the points of intersection of the line $x + y = 15$ and the parabola $y = {x^2} - 6x + 1$

Answer

$\left( {7,8} \right)$ and $\left( { - 2,17} \right)$

Worked Solution

Question 20

51952

Find the point of intersection of the hyperbola $y=\dfrac{4}{x}$ and the straight line $y=x+3$

Answer

$(1,4) \text { and }(-4,-1)$

Worked Solution