Algebra
Questions
Which of the following systems of linear equations has no solution?
A) y = 6x + 3 B) y = 10
y = 6x + 9 y = 10x + 10
C) y = 14x + 14 D) x = 3
y = 10x + 14 x = 10
Q1
Skill Systems of two linear equations in two variable
Difficulty
Q2
A line in the xy-plane has a slope of 9 and passes through the point(0,-5) . The equation y = px + r defines the line, where p and r are constants. What is the value of p?
Skill Systems of two linear equations in two variable
Difficulty
Q3
The table shows four values of x and their corresponding values of f(x) . There is a linear relationship between x and f(x) that is defined by the equation f(x) = mx - 28, where m is constant. What is the value of m?
Skill Systems of two linear equations in two variable
Q4
A line passes through the points (4,6) and (15,24) . What is the slope of the line?
Q5
What is the solution ( x , y) to the given system of equations?
y - 9x = 13
5x = 2y
Skill Systems of two linear equations in two variable
A) 5/2 , 1
B) 1 , 2/5
C) -2 , -5
D) -5 , -2
Q6
Figure A and figure B are both regular polygons. The sum of the perimeter of figure A and the perimeter of figure B is 63 inches. The equation 3x + 6y = 63 represents this situation, where x is the number of sides of figure A and y is the number of sides of figure B. Which statement is the best interpretation of 6 in this context?
Skill Systems of two linear equations in two variable
A) Each side of figure B has a length of 6 inches.
B) The number of sides of figure B is 6.
C) Each side of figure A has a length 6 of inches
D) The number of sides of figure A is 6.
Q7
If 46 = 16 + 2( x - 8 ), what is the value of 2( x - 8) ?
A) 16
B) 23
Skill Systems of two linear equations in two variable
C) 30
D) 38
Q8
A model estimates that whales from the genus Eschrichtius travel 72 to 77 miles in the ocean each day during their migration. Based on this model, which inequality represents the estimated total number of miles, ,x, a whale from the genus Eschrichtius could travel in days of its migration?
Skill Systems of two linear equations in two variable
A) 72 + 16 ≤ x ≤ 77 + 16
B) 72 (16 ) ≤ x ≤ 77 ( 16 )
C) 72 ≤ x + 16 ≤ 77
D) C) 72 ≤ 16(x ) ≤ 77
Q9
The solution of the given system of equation is ( x , y ). What is the value of y?
6x + 7y = 28
2x + 2y = 10
Skill Systems of two linear equations in two variable
A) -2
B) 7
C) 14
D) 18
Q10
The solution of the given system of equation is ( x , y ). What is the value of x?
y = - (1/5)x
y = (1/7)x
Skill Systems of two linear equations in two variable
A) 5
B) 0
C) 2
D) 7
Q11
A batch of banana milkshakes consists of 4 cups of ice cream and 2 bananas and has 1,114 milligrams (mg) of calcium. There is 276 mg of calcium in 1 cup of the ice cream used to make this batch of milkshakes. How much calcium, in mg , is in 1 banana?
Skill Systems of two linear equations in two variable
A) 5
B) 10
C) 419
D) 1,104
Q12
What is the slope of the graph of y = 1/4(27x + 15) + 7x in the xy-plane ?
Skill Systems of two linear equations in two variable
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Q13
The function f gives the monthly fee f(x), in dollars, a facility charges to keep x crates in storage. What is the monthly fee, in dollars, the facility charges to keep 50 crates in storage?
f(x) = 45x + 600
Skill Systems of two linear equations in two variable
Q14
Line r is defined by the equation 4x - 9y = 3. Line s is parallel to line r in the xy-plane. What is the slope of line s ?
A) 9/4
C) -4
B) 4/9
Skill Systems of two linear equations in two variable
Q15
D) -9
At how many points do the graph of the given equations intersect in the xy-plane ?
y = 2x + 10
y = 2x - 1
A) Zero
C) Exactly two
B) Exactly one
Skill Systems of two linear equations in two variable
Q16
D) Infinitely many
3x + 6 = 4y
3x +4 = 2y
The solution of the given system of equations is ( x , y ). What is the value of y ?
Skill Systems of two linear equations in two variable
Q17
If 9(4 - 3x) + 2 = 8( 4 - 3x ) + 18, what is the value of 4 - 3x ?
A) -16
C) 4
B) -4
D) 16
Skill Systems of two linear equations in two variable
Q18
2a + 8b = 198
2a + 4b = 98
The solution of the given system of equations is ( a , b ). What is the value of b ?
Skill Systems of two linear equations in two variable
Q19
A company that creates and sells tape dispensers calculates its monthly profit, in dollars, by subtracting its fixed monthly costs, in dollars, from its monthly sales revenue, in dollars. The equation 15,000 = 2.00x - 4,500 represents this situation for a month where tape dispensers are created and sold. Which statement is the best interpretation of 2.00x in this context ?
Skill Systems of two linear equations in two variable
A) The monthly sales revenue, in dollars, from selling x tape dispensers
B) The monthly sales revenue, in dollars, from each tape dispenser sold
C) The monthly sales revenue, in dollars, of creating each tape dispenser
Q20
D) The monthly sales revenue, in dollars, of creating x tape dispenser
Line k is defined by y = - ( 17 / 3 )x + 5. Line j is perpendicular to line k in xy plane. What is the slope of line j?
Skill Systems of two linear equations in two variable
Q22
Q23
Q24
Q25
Which equation defines the linear function f ?
A) f (x) = -13x - 11
B) f (x) = -2x + 7
C) f (x) = -13x + 7
D) f(x) = -2x - 11
When line n is graphed in the xy-plane, it has an x-intercept of (-4 , 0) and a y - intercept of (0 , 86/3 ). What is the slope of line n?
A) 3/344
C) 43/6
If f(x) = x + 7 and g (x) = 7x , what is the value of 4f( 2 ) - g ( 2 ) ?
A) -5
C) 22
Let p is defined by 2y + 18x = 9. Line r is perpendicular to line p in the xy - plane. What is the slope of the line r?
A) -9
C) 1/9
A total of 2 squares each have side length r. A total of 6 equilateral triangles each have side length t . None of these squares and triangles shares a side. The sum of the perimeters of all these squares and triangles is 210. Which equation represents this situation?
A) 6r + 24t = 210
C) 8r + 18t = 210
