SAT Math: systems of Non linear equations in two variables-Practice Questions

Question

The graph of a linear equation and the graph of a quadratic equation are shown. What is true about the point (−1,4)?

  1. The point satisfies only the quadratic equation
  2. The point satisfies only the linear equation.
  3. The point satisfies both equations.
  4. The point satisfies neither equation.
Answer/Explanation

Ans: C

 

Question

\(y=(x+3)(x-7)\)
\(y=x-7\)
If \((x,y)\) is a solution to the given system of equations, which of the following could be the value of \(x\)? 

  1. -7
  2. -3
  3. 3
  4. 7
Answer/Explanation

Ans: D

Question

A system of equations consists of a quadratic equation and a linear equation. The equations in this system are graphed in the \(xy\)-plane above. How many solutions does the system have?

  1. 0
  2. 1
  3. 2
  4. 3
Answer/Explanation

Ans: C

Question

In the \(xy\)-plane, a parabola has vertex (3, 1) and intersects the \(x\)-axis at two points. If the equation of the parabola is written in the form \(y = ‐ax^2 +bx + c\), where \(a, b\), and \(c\) are constants, which of the following could be a value of \(c\)?

  1. -8
  2. 2
  3. 3
  4. 7
Answer/Explanation

Ans: A

Question

In the \(xy\)-plane, what is the \(y\)-coordinate of the point of intersection of the graphs of \(y = (x ‐ 1)^2\) and \(y = 2x ‐ 3\)? 

Answer/Explanation

Ans: 1

Question

\(x-y=1\)
\(x+ y=x^2 -3\)
Which ordered pair is a solution to the system of equations above? 

  1. \((1+\sqrt{3},3)\)
  2. \((\sqrt{3},-\sqrt{3})\)
  3. \((1+\sqrt{5},\sqrt{5})\)
  4. \((\sqrt{5},-1+\sqrt{5})\)
Answer/Explanation

Ans: A

Question

\((x+2)^2+(y-3)^2=40\)

\(y=-2x+4\)

Which of the following could be the \(x\)-coordinate of a solution to the system of equations above? 

  1. \(\sqrt{7}\)
  2. \(\frac{\sqrt{35}}{2}\)
  3. \(\frac{6+2\sqrt{34}}{5}\)
  4. \(\frac{4+\sqrt{191}}{5}\)
Answer/Explanation

Ans: A

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