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1 year ago

How many solutions exist for the system of equations graphed below?

Mathematics

2 answers:

Zinaida [17]1 year ago

6 0

Answer:

one

Step-by-step explanation:

When a system of equations is graphed, the solution is the coordinate that is plotted at the intersection of the two lines.

If the two lines cross once, there is only one solution.

If the two lines are on top of each other then there are infinitely many solutions.

If the two lines are parallel ( and never touch ) then there are no solutions

By looking at the graph we notice the two lines intersect once. So we can conclude that there is only one solution.

Andreas93 [3]1 year ago

5 0

Answer: b) one

Detailed Explanation:

For the graph of a system of linear equations :-

• If the lines are parallel, then the pair of equations has no solution
• If the lines are coincident, then the pair of equations has infinite solutions
• If the lines are intersecting, then the pair of equations have one solution.

In this graph, the lines formed by the equations are intersecting at a point. Hence it has a unique solution.

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2 years ago

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Without drawing the graphs, find the points of intersection of the lines: a 7x+4y=23 and 8x–10y=19

emmainna [20.7K]

Answer:

(3,0.5)

Step-by-step explanation:

The given system has equations:

$7x + 4y = 23 \\ 8x - 10y = 19$

Let us multiply the second equation by 4 and the first equation by 10.

$70x + 40y = 230 \\ 32x - 40y = 76$

We add both new equations to get:

$102x = 306 \\ x = \frac{306}{102} = 3$

Put x=3 into the first equation and solve for y.

$7(3) + 4y = 23 \\ 21 + 4y = 23 \\ 4y = 23 - 21 \\ 4y = 2 \\ y = \frac{1}{2}$

The point of intersection is the solution to the system of equation which is (3,0.5)

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3 years ago

A trucking company uses matrix A , shown below, to represent the driving time in hours for 6 trucking routes. A = [ 4 6 8 ]

zepelin [54]

Each element of the matrix are multiplied by the scalar to form a matrix of

same size as the original matrix in matrix scalar multiplication.

$60 \cdot A = \left[\begin{array}{ccc}240\4&360&480\\360&480&600\end{array}\right]$

Reasons:

The matrix <em>A</em> is presented as follows;

$A = {\left[\begin{array}{ccc}4&6&8\\6&8&10\end{array}\right]}$

Using the multiplication of a matrix and a scalar, we have;

$60 \cdot A = 60 \cdot \left[\begin{array}{ccc}4&6&8\\6&8&10\end{array}\right] = \left[\begin{array}{ccc}60 \times 4&60 \times 6&60 \times 8\\60 \times 6&60 \times 8&60 \times 10\end{array}\right] = \left[\begin{array}{ccc}\mathbf{240}&\mathbf{360}&\mathbf{480}\\\mathbf{360}&\mathbf{480}&\mathbf{600}\end{array}\right]$