Solving Systems of Equations by Substitution Warmup 3

Solve the system of equations.

• (11, 21)

• (3, 11)

• (11, -67)

• No solution

• Infinite solutions

Answer explanation

To solve the system of equations, substitute values from the answer choices into the equations. (11, 21) satisfies both equations, confirming it as the correct solution.

Solve the system of equations.

• (-6, 1)

• (0, 0)

• (1, -6)

• No solution

• Infinite solutions

Answer explanation

The system of equations has the same slope and y-intercept, indicating they are identical lines. Therefore, there are infinite solutions where the lines overlap.

Solve the system of equations.

• (3, 33)

• (7, 77)

• (2, 22)

• No solution

• Infinite solutions

Answer explanation

The system of equations has no point of intersection, indicating that the lines are parallel. Therefore, the correct answer is 'No solution'.

The first step in solving using the substitution method is __________.

• get x by itself

• get y by itself

• get either variable by itself

• add the equations together

Answer explanation

The first step in the substitution method is to get either variable by itself. This allows you to express one variable in terms of the other, making it easier to substitute into the other equation.

An ordered pair that satisfies both equations in a system of linear equations is called a ​ (a)   to the system of equations.

• solution

• coordinate

• inconsistent

• input

Answer explanation

An ordered pair that satisfies both equations in a system is called a 'solution'. This term specifically refers to the values that make both equations true, distinguishing it from other terms like 'coordinate' or 'input'.

• 5x+5x+10=16

• -5x-20=16

• 5x-10x-20=16

• 5x+2x+12=16

Answer explanation

To isolate x in the first equation, substitute y from the second equation: 5x - 2(5x + 10) = 16 simplifies to -5x - 20 = 16 and 5x - 10x - 20 = 16. Thus, the correct choices are -5x-20=16 and 5x-10x-20=16.