# Linear Equations in Two Variables - Examples, Exercises and Solutions

A linear equation is an equation of the type:
$y=ax+b$

A system of two linear equations with two unknowns is a pair of adjacent linear equations or written one below the other, either within braces or without graphic signs.

To solve a system of equations, several steps must be taken:

• Isolate the variables in all the equations.
• Place possible values to the isolated variables (for example $Y=0,1,2$.
• Compare two equations (it is advisable to illustrate them on a graph).
• Find the point of intersection of the two equations.

## Practice Linear Equations in Two Variables

### Exercise #1

Solve the following equations:

$(I)x+y=18$

$(II)y=13$

### Video Solution

$x=5,y=13$

### Exercise #2

Solve the following equations:

$(I)2x+y=9$

$(II)x=5$

### Video Solution

$x=5,y=-1$

### Exercise #3

Solve the following system of equations:

$\begin{cases} x-y=5 \\ 2x-3y=8 \end{cases}$

### Video Solution

$x=2,y=-3$

### Exercise #4

Solve the above set of equations and choose the correct answer.

$(I)-2x+3y=4$

$(II)x-4y=8$

### Video Solution

$x=-8,y=-4$

### Exercise #5

Solve the above set of equations and choose the correct answer.

$(I)-5x+4y=3$

$(II)6x-8y=10$

### Video Solution

$x=-4,y=-4\frac{1}{4}$

### Exercise #1

Find the value of x and and band the substitution method.

$(I)x+and=5$

$(II)2x-3and=-15$

### Video Solution

$x=0,y=5$

### Exercise #2

Find the value of x and and band the substitution method.

$(I)-x-2and=4$

$(II)3x+and=8$

### Video Solution

$x=4,y=-4$

### Exercise #3

Solve the above set of equations and choose the correct answer.

$(I)-8x+3y=7$

$(II)24x+y=3$

### Video Solution

$x=0.025,y=2.4$

### Exercise #4

Solve the above set of equations and choose the correct answer.

$(I)7x-4y=8$

$(II)x+5y=12.8$

### Video Solution

$x=2.33,y=2.09$

### Exercise #5

Solve the following system of equations:

$\begin{cases} -8x+5y=3 \\ 10x+y=16 \end{cases}$

### Video Solution

$x=1.32,y=2.8$

### Exercise #1

Find the value of x and and band the substitution method.

$(I)-x+3and=12$

$(II)4x+2and=10$

### Video Solution

$x=\frac{3}{7},y=\frac{29}{7}$

### Exercise #2

Find the value of x and and band the substitution method.

$(I)-5x+9and=18$

$(II)x+8and=16$

### Video Solution

$x=0,y=2$

### Exercise #3

Solve the above set of equations and choose the correct answer.

$(I)\frac{1}{3}x-4y=5$

$(II)x+6y=9$

### Video Solution

$x=11,y=-\frac{1}{3}$

### Exercise #4

Solve the following system of equations:

$\begin{cases} 2x-\frac{1}{5}y=18 \\ 3x+y=6 \end{cases}$

### Video Solution

$x=7.38,y=-16.14$

### Exercise #5

Find the value of x and and band the substitution method.

$(I)-4x+4and=15$

$(II)2x+8and=12$

### Video Solution

$x=-\frac{9}{5},y=\frac{39}{20}$