Jerome bought 15 videos from a department store. Some videos were new releases, x, which cost $19, and some videos were classics, y, which cost $8. He spent a total of $164 on the videos. Which system of equations is set up correctly to model this information?
A(x + y = 15. 19 x + 8 y = 164.
B(x + y = 15. 8 x + 19 y = 164.
C(x + y = 164. 19 x + 8 y = 15.
D(x + y = 15. 19 x minus 8 y = 164.
B(x + y = 15. 8 x + 19 y = 164.) is set up correctly to model this information.
The equation x + y = 15 represents the fact that Jerome bought a total of 15 videos.
The equation 8y + 19x = 164 represents the total cost of the videos. This equation takes into account the different prices of the new releases (x) and classics (y), with each new release costing $19 and each classic costing $8.
Setting up the equation as 8y + 19x = 164 instead of 19y + 8x = 164 makes more sense since y is associated with the lower-priced classics, and thus, should be multiplied by the lower price of $8.
Which system of linear equations has the ordered pair (4, –5) as a solution?
2 x minus 5 y = negative 30 and 7 x + 4 y = negative 19
6 x minus y = negative 29 and 8 x + 3 y = negative 17
3 x minus 2 y = 22 and 2 x + 9 y = negative 37
5 x minus 6 y = 49 and x + 8 y = negative 27
The system of linear equations that has the ordered pair (4, –5) as a solution is:
6 x - y = -29 and 8 x + 3 y = -17.
To check, we can substitute x = 4 and y = -5 into each equation:
6(4) - (-5) = 24 + 5 = 29, which is the left-hand side of the first equation. So (4, -5) is a solution to the first equation.
8(4) + 3(-5) = 32 - 15 = 17, which is the left-hand side of the second equation. So (4, -5) is a solution to the second equation.
Therefore, the system of equations with the ordered pair (4, –5) as a solution is:
6 x - y = -29 and 8 x + 3 y = -17.
In this system of equations, which variable would it be easiest to solve for?
x + 3 y = 13. 3 x + 2 y = 25.
The easiest to solve for is x in the first equation.
The easiest to solve for is y in the first equation.
The easiest to solve for is x in the second equation.
The easiest to solve for is y in the second equation.
The easiest to solve for is x in the first equation.
To solve for x in the first equation x + 3y = 13, we can simply subtract 3y from both sides to get x = 13 - 3y.
This gives us an expression for x in terms of y, which we can substitute into the second equation 3x + 2y = 25 to eliminate x and solve for y.
Solving for y in the first equation or x in the second equation would require more steps and potentially more complicated algebraic manipulations.
The graphed line shown below is y = negative 4 x minus 12.
On a coordinate plane, a line goes through (negative 3, 0) and (negative 2, negative 4).
Which equation, when graphed with the given equation, will form a system that has no solution?
y = 4 x + 12
y = negative 4 x
y = negative 12
y = negative 4 (x + 3)
The equation that, when graphed with the given equation, will form a system that has no solution is:
y = 4x + 12
To see why, we can first graph the given equation y = -4x - 12:
Then, we can graph the equation y = 4x + 12:
We can see that the two lines are parallel and will never intersect. Therefore, the system of equations y = -4x - 12 and y = 4x + 12 has no solution.
The other equations given do not create parallel lines when graphed with y = -4x - 12 and will therefore have a solution when combined with the given equation.
What is the solution to the system of linear equations graphed below?
On a coordinate plane, 2 lines intersect at (3.5, negative 4).
(3 and one-half, negative 4)
(Negative 4, 3 and one-half)
(0, 3)
(0, negative 4)
The solution to the system of linear equations graphed below is:
(3 and one-half, negative 4)
This is the point where the two lines intersect on the coordinate plane, as given in the question stem.
Which ordered pair is the solution to the system of linear equations y = negative 7 x + 2 and y = 9 x minus 14?
(negative 5, 1)
(1, negative 5)
(5, negative 1)
(Negative 1, 5)