# Simultaneous equations (Systems of linear equations): Problems with Solutions

Problem 1
Is the point $(0 ,\frac{5}{2})$ a solution to the following system of equations?

$\begin{cases}5x +2y =1 \\ -3x +3y = 5\end{cases}$
Problem 2
Is the point $(1 ,3)$ a solution to the following system of equations?

$\begin{cases}2x -y = -1 \\ 3x +y =6\end{cases}$
Problem 3
The graph represents the system of equations
$\begin{cases}3x -4y = -6 \\ 2x +4y =16\end{cases}$

Choose the correct statement:

Problem 4
The graph represents the system of equations
$\begin{cases}x +y =1 \\ 2x +2y =2\end{cases}$

Choose the correct statement:

Problem 5
The following graph represents the system of equations
$\begin{cases}x +y =3 \\ 2x +2y =2\end{cases}$

Choose the correct statement:

Problem 6
Which of the following points on the plane are solutions?
How many solutions do the system have?

$\begin{cases}y -2x =1 \\ 6x -3y = -3\end{cases}$
Problem 7
The system has infinite number of solutions, does this mean that any point on the plane is the solution of the system?
(Hint: take any point (a, b) and substitute these values in the system, which you can conclude)

$\begin{cases}x +2y =1 \\ 3x +6y =3\end{cases}$
Problem 8
Solve the following system by graphing

$\begin{cases}4x +y =4 \\ 3x +\frac{1}{2}y =2\end{cases}$

You are not allowed to provide an answer.
Problem 9
Which of the following systems is represented in the image?

Problem 10
Solve the simultaneous equations by substitution
$\left\{\begin{array}{c} -10x -5y =0 \\ 21x -7y =28\end{array}\right.$

Problem 11
Solve the simultaneous equations by substitution
$\left\{\begin{array}{c}x +y =3 \\ 2x -y =0\end{array}\right.$
Problem 12
Solve the following system using equalization method.
$\begin{cases}{c}5x -\frac{1}{2}y = -1 \\ 3x -2y =1\end{cases}$
Problem 13
Solve the system of equations using addition.

$\begin{cases}\frac{1}{3}x +\frac{1}{5}y =\frac{2}{7} \\ \frac{1}{2}x +\frac{1}{10}y =\frac{3}{7}\end{cases}$
Problem 14
Solve the following system of linear equations using equalization
$\begin{cases}5x -\frac{1}{2}y = -1 \\ 3x -2y =1\end{cases}$
Problem 15
Solve the following system of equations using addition.
$\begin{cases}2x +3y = -1 \\ 3x +4y =0\end{cases}$
Problem 16
The double of the sum of two numbers is 32 and their difference is 0. What are the numbers?
Problem 17
Let we have two numbers whose sum is 0. If we add 123 to one of them, we get twice as large as the other.
What are the numbers?
Problem 18
A farm has pigs and turkeys. There are 58 heads and 168 legs in total. How many pigs and turkeys are there?
Problem 19
John said: "I have double the amount of money you have" and Peter answered: "If you give me six dollars, we will have the same amount of money". How much money do each of them have?

Correct:
Wrong:
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