# 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.

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

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

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

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 $$y = 2x ‐ 3$$?

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. $$(\sqrt{5},-1+\sqrt{5})$$

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. $$\frac{4+\sqrt{191}}{5}$$