System of Equations

Solve the system by substitution.

−x + 5y = 12

y = −2x − 2

• (−2, −7)

• (−2, 2)

• (−2, −2)

• (2, −2)

Solve the system by elimination.

7x - y = -10

-7x + 5y = -6

• (-2, -4)

• (-2, -1)

• (-4, -1)

• (6, -8)

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

When you graph the exact same equation twice,

• you will have no solution. 

• you will have one solution.

• you will have infinite solutions. 

• you will graph a giraffe. 

What does it mean when a system of linear equations has a unique solution?

• The graphs of the equations intersect at a single point

• The graphs of the equations are parallel and do not intersect

• The graphs of the equations coincide, meaning they are the same line

• The graphs of the equations intersect at infinitely many points

What is the 'method of elimination' in solving systems of linear equations?

• It involves solving one of the equations for one variable and then substitifying that expression into the other equation

• It involves graphing the equations on the same set of axes and finding the point(s) of intersection

• It involves adding or subtracting the equations in order to eliminate one of the variables

• It involves multiplying each equation by a suitable number so that the two equations have the same or opposite coefficients for one variable

What does it mean when a system of linear equations has infinitely many solutions?

• The graphs of the equations intersect at a single point

• The graphs of the equations are parallel and do not intersect

• The graphs of the equations coincide, meaning they are the same line

• The graphs of the equations intersect at infinitely many points

What is a 'system of equations'?

• A set of two or more equations that contain two or more variables

• When a system of two equations has graphs that never intersect because lines are parallel

• To replace a variable with a number or another expression in an algebraic expression

• Algebraic process of eliminating a variable in a system of equations by combining the equations through addition

What is the process of 'elimination' in algebra?

• When the graphs of two linear equations overlap and intersect at infinitely many points

• When a system of two equations has graphs that never intersect because lines are parallel

• To replace a variable with a number or another expression in an algebraic expression

• Algebraic process of eliminating a variable in a system of equations by combining the equations through addition

What is the definition of 'solution of a system of equations'?

• A set of values that make all equations in a system true

• When a system of two equations has graphs that never intersect because lines are parallel

• To replace a variable with a number or another expression in an algebraic expression

• Algebraic process of eliminating a variable in a system of equations by combining the equations through addition