AnswersAlgebra IISolving One-Variable Equations with Systems

Solving One-Variable Equations with Systems — Quiz Answers

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1
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Which graph can be used to find the solution(s) to x squared minus 4 x plus 4 is equal to 2 x plus 1 plus x squared ?

A
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. There are two parabolas. One of them parabola opens up, has the vertex at (2 comma 0), passes through (0 comma 4) and (4 comma 4). The other parabola opens down, has the vertex at (1 comma 0), and passes through (negative 1 comma negative 4) and (3 comma negative 4).
B
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit.There are two parabolas. One of them opens up, has the vertex at (negative 2 comma 0), passes through (negative 2 comma 2) and (2 comma 2). The other parabola opens down, has the vertex at (1 comma 0), and passes through (negative 1 comma negative 4) and (3 comma negative 4).
C
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. There are two parabolas and both the parabolas open up. One of them has the vertex at (2 comma 0), passes through (0 comma 4) and (4 comma 4). The other parabola has the vertex at (negative 1 comma 0), and passes through (1 comma 4) and (negative 3 comma 4).
D
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. There are two parabolas and both open up. One of them has the vertex at (1 comma 0), passes through (0 comma 2) and (2 comma 2). The other parabola has the vertex at (negative 1 comma 0), and passes through (negative 2 comma 4) and (0 comma 4).
2
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Which system of equations can be graphed to find the solution(s) to x squared is equal to 2 x plus 3 ?

A
y is equal to x squared plus 2 x plus 3 y is equal to 2 x plus 3
B
y is equal to x squared minus 3 y is equal to 2 x plus 3
C
y is equal to x squared minus 2 x minus 3 y is equal to 2 x plus 3
D
y is equal to x squared y is equal to 2 x plus 3
3

What is the solution of 3 x plus 5 is equal to 2 x minus 7 ?

A
the x -coordinates of the x -intercepts of the lines y is equal to 3 x plus 5 and y is equal to 2 x minus 7
B
the x -coordinate of the intersection point of the lines y is equal to 3 x plus 5 and y is equal to 2 x minus 7
C
the y -coordinate of the intersection point of the lines y is equal to 3 x plus 5 and y is equal to 2 x minus 7
D
the y -coordinates of the y -intercepts of the lines y is equal to 3 x plus 5 and y is equal to 2 x minus 7
4

What are the two solutions of x squared minus 2 x minus 4 is equal to negative 3 x plus 9 ?

A
the x -coordinates of the x -intercepts of the graphs of y is equal to x squared minus 2 x minus 4 and y is equal to negative 3 x plus 9
B
the x -coordinates of the intersection points of the graphs of y is equal to x squared minus 2 x minus 4 and y is equal to negative 3 x plus 9
C
the y -coordinates of the intersection points of the graphs of y is equal to x squared minus 2 x minus 4 and y is equal to negative 3 x plus 9
D
the y -coordinates of the y -intercepts of the graphs of y is equal to x squared minus 2 x minus 4 and y is equal to negative 3 x plus 9
5

Tiffany is solving an equation where both sides are quadratic expressions. She sets each quadratic equation equal to y and graphs the resulting system. If the graph of one quadratic opens upward and the other opens downward, what is the greatest possible number of intersections for these graphs?

A
none
B
two
C
one
D
infinitely many
6

Heather is solving an equation by graphing the expressions on either side of the equal signs. If the graph intersects at an infinite number of points, which statement could describe the equation Heather is attempting to solve?

A
One side of the equation is a linear expression, and the other side of the equation is a quadratic expression.
B
One side of the equation is a constant, and the other side of the equation is a quadratic expression.
C
One side of the equation is a constant, and the other side of the equation is a linear expression.
D
One side of the equation is a quadratic expression, and the other side of the equation is a quadratic expression.
7

What are the two solutions of 2 x squared is equal to negative x squared minus 5 x minus 1 ?

A
the y -coordinates of the intersection points of the graphs of y is equal to 2 x squared and y is equal to negative x squared minus 5 x minus 1
B
the y -coordinates of the y -intercepts of the graphs of y is equal to 2 x squared and y is equal to negative x squared minus 5 x minus 1
C
the x -coordinates of the intersection points of the graphs of y is equal to 2 x squared and y is equal to negative x squared minus 5 x minus 1
D
the x -coordinates of the x -intercepts of the graphs of y is equal to 2 x squared and y is equal to negative x squared minus 5 x minus 1
8

Which graph can be used to find the solution(s) to x squared minus 1 is equal to x plus 1 ?

A
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. A line passes through the origin and (1 comma 1). A parabola opens up, has vertex at (0 comma negative 1) and cuts the x-axis at (negative 1 comma 0) and (1 comma 0).
B
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. A line passes through (0 comma 1) and (negative 1 comma 0). A parabola opens up, has vertex at (0 comma negative 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).
C
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. A line passes through (0 comma 1) and (negative 1 comma 0). A parabola opens down, has vertex at (0 comma 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).
D
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. A line passes through the origin and (1 comma 1). A parabola opens down, has vertex at (0 comma 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).
9

Which graph can be used to find the solution(s) to x squared minus 1 is equal to 3 ?

A
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. A line passes through the (negative 3 comma 0) and (0 comma 3). A parabola opens up, has vertex at (0 comma negative 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).
B
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 9 to 9 with an interval of 1 unit. A line is parallel to the x axis and cuts the y axis at (0 comma 3). A parabola opens up, has vertex (0 comma negative 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).
C
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 9 to 9 with an interval of 1 unit. A line is parallel to the y axis and cuts the x axis at (3 comma 0). A parabola opens up, has vertex (0 comma negative 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).
D
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 9 to 9 with an interval of 1 unit. A line passes through the origin and (1 comma 3). A parabola opens up, has a vertex (0 comma negative 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).
10

Which system of equations can be graphed to find the solution(s) to 2 minus 9 x is equal to x over 2 minus 1 ?

A
y is equal to 9 x y is equal to negative x over 2
B
y is equal to 2 minus 9 x y is equal to negative open paren x over 2 minus 1 close paren
C
y is equal to negative 9 x y is equal to x over 2
D
y is equal to 2 minus 9 x y is equal to x over 2 minus 1

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