Exploring Systems of Linear Equations

Consider the system of linear equations 2x + 3y = 8 and 3x + y = –2. Which statement is correct?

• The point (1, 2) is not a solution to the system of equations because it satisfies neither equation

• The point (1, 2) is not a solution to the system of equations because it does not satisfy the equation 3x + y = –2.

• The point (1, 2) is a solution to the system of equations because it satisfies the equation 2x + 3y = 8.

• The point (1, 2) is a solution to the system of equations because it satisfies both equations.

Which ordered pair is a solution to the system of linear equations -4x+y=8 and x-5y=17?

• (–4, –3)

• (–4, 3)

• (–3, –4)

• (–3, 4)

Betty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations 6x+5y=7 and x+4y=17. Based on this information, which statement is correct?

• (–3, 5) satisfies neither the equation 6x + 5y = 7 nor the equation x + 4y = 17.

• (–3, 5) satisfies the equation 6x + 5y = 7 but not the equation x + 4y = 17.

• (–3, 5) satisfies the equation x + 4y = 17 but not the equation 6x + 5y = 7.

• (–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.

Which ordered pair is the solution to the system of linear equations y= -7x+2 and y= 9x-14?

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Which ordered pair is the solution to the system of linear equations -5x+y=26 and 2x-7y=16 ?

• (–4, 6)

• (6, –4)

• (–4, –6)

• (–6, –4)

Which ordered pair is a solution to the system of linear equations 1/2x - 3/4y= 11/60 and 2/5x + 1/6y = 3/10 ?

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Which system of linear equations has the ordered pair (4, –5) as a solution?

• $2x-5y=-30\ and\ 7x+4y=-19$

• $6x-y=-29\ and\ 8x+3y=-17$

• $3x-2y=22\ and\ 2x+9y=-37$

• $5x-6y=49\ and\ x+8y=-27$

Tina wrote the equations 3x-y=9 and 4x+y=5. What can Tina conclude about the solution to this system of equations?

• (–3, 2) is a solution to the system of linear equations.

• (–2, 3) is a solution to the system of linear equations.

• (2, –3) is a solution to the system of linear equations.

• (3, –2) is a solution to the system of linear equations.

The solution to a system of linear equations is (-3,-3) . Which system of linear equations has this point as its solution?

• $x-5y=-12\ and\ 3x+2y=-15$

• $x-5y=-12\ and\ 3x+2y=15$

• $x-5y=12\ and\ 3x+2y=-15$

• $x-5y=12\ and\ 3x+2y=15$

The system of linear equations 5x+3y=3 and x+y= -1 is graphed below.

What is the solution to the system of equations?

• (–4, 3)

• (–3, 4)

• (3, –4)

• (4, –3)