Algebra 1 Final REview

What is the solution to the system of equations?

4x-y=3

3x+y=4

(​ (a)   ,​ (b)   )

• 1

• 2

• 3

• 4

• 5

• 6

• 7

• 8

• 9

• 0

Answer explanation

To solve the system of equations, add the two equations to eliminate y. This gives 7x = 7, so x = 1. Substitute x=1 into one of the equations to find y=1. Therefore, the solution is (1, 1).

In this system

x+3y=9

4x-2y=-6

it'll be easiest to start by solving the first equation for x.

The result of doing so is x=​9-3y.

Fill in the blanks to plug that expression in and solve for y:

4(​9-3y)-2​y =-6

36-​12y-2y=​-6

36-​14y =-6

-14y=​ (a)  

y=​ (b)  

• -42

• 3

• 30

• -3

Answer explanation

To solve for y, substitute x=9-3y into the second equation: 4(9-3y)-2y=-6. Simplify to get -14y=-42, then solve for y to get y=3. Therefore, the correct answer is 3.

Consider the system

4x+3y=-1

5x+4y=1

After we do this multiplication, what will the new equations be?

​ 4(4x+3y=-1) ---> ​ (a)   x +​ (b)   y=​ (c)  

​-3(5x+4y=1)​ ---> ​ (d)   x -​ (e)   y= -3

• 16

• 12

• -4

• -15

• 3

• 5

• 1

• -1

• -12

• -3

Answer explanation

After multiplying the first equation by 4, we get 16x + 12y = -4. Multiplying the second equation by -3 gives -15x - 12y = -3.

Consider the system

4x+3y=-1

5x+4y=1

Let's say I want to eliminate the y's. What is the least common multiple of 3 and 4?

LCM = ​ (a)  

Multiply each equation by a number so that the coefficient of y will be 12, with one positive and one negative.

​ (b)   (4x+3y=-1)

​ (c)   (5x+4y=1)

• 12

• 4

• -3

• 3

• 5

• 1

• -1

• -12

Answer explanation

To eliminate the y's, the least common multiple of 3 and 4 is 12. Multiply the first equation by 4 and the second by -3 to get 12y and -12y respectively.

Mathematical Equivalence

ON

Tags

A.11B

Mathematical Equivalence

ON

Simplify:

Mathematical Equivalence

ON

What is the vertex of the quadratic function:
y = x² - 6x + 11?

• (3,2)

• (-3,-2)

• (-3,2)

• (3,-2)

Answer explanation

The vertex of a quadratic function in the form y = ax^2 + bx + c is given by (-b/2a, f(-b/2a)), so for y = x^2 - 6x + 11, the vertex is (3,2).

Determine the vertex of the parabola:
y = 5x² - 20x + 13

• (2, 7)

• (-2, -7)

• (2, -7)

• (-7, 2)

Answer explanation

The vertex of a parabola in the form y = ax^2 + bx + c is given by the point (-b/2a, f(-b/2a)). Substituting a=5, b=-20 into the formula gives the vertex as (2, -7). Therefore, the correct answer is (2, -7).

Find the Vertex: y= -5x² -20x - 26

• (-2, -6)

• (-2, 6)

• (6,-2)

• (-2, 3)

Answer explanation

To find the vertex, use the formula x = -b / 2a. In this case, a = -5, b = -20. Plugging in the values, x = -(-20) / 2(-5) = -20 / -10 = 2. Then substitute x back into the equation to find y. Therefore, the vertex is (-2, -6).