Solving pairs of linear equations in two variables

Using elimination method, what will be the value of (x, y) after solving

-x - y = 5 and -x + 4y = 15?

 $-2x\ +\ 2y\ =18$  
 $\ 2x\ +\ 6y\ =\ \ 6$  

•  $\left(-6,3\right)$  

•  $\left(6,3\right)$  

•  $\left(6,-3\right)$  

• Infinite number of solutions

Use linear combinations to find the solution to this system of linear equations:

 $x-y=11$  
 $2x+y=19$  

• (10, -1)

• (-1, 10)

• (7, -4)

• (-4, 7)

Which variable will be eliminated?

4x+9y=28

4x-y=-28

• all of the variables

• none of the variables

• y

• x

Solve this system

of linear equations by elimination.

3x - 4y = 14

5x + y = 8

• ( -2, 2 )

• ( 2, -2 )

• ( 2, 2 )

• ( -2, -2 )

Solve the system of equations:

3x+4y=8

3x+2y=10

• (4,-1)

• (-3,2)

• (8,-10)

• (-1,-4)

A system involving two variables (x and y), each linear equation is called a

• System of Linear Equations

• Solution of a Linear Inequalities

• System of Linear Inequalities

• Solution of a Linear Equations

What is the elimination method?

• Both equations are in slope - intercept form

• A method of solving a system of equations by replacing one variable with an equivalent expression containing the other variable.

• solving systems by adding or subtracting equations to eliminate a variable

Determine the solution to the following system of equations using algebraic methods: 2x - 3y = 6 4x + 5y = 3

• x = 3/2, y = 1/2

• x = 45/22, y = -9/11

• x = 45/22, y = -9/11

• x = -1/4, y = 1/8

Solve using Elimination: 3x+y=9 and 5x+4y=22

• (2,3)

• (3,2)

• (0,2)

• Impossible to solve.