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Norma-Jean [14]
3 years ago
11

Solve the system of equations using substitution.

Mathematics
2 answers:
tresset_1 [31]3 years ago
8 0

Answer:

The system of equations has no solution

Step-by-step explanation:

The method of substitution consists in solving one equation for a variable and replacing it in the other equation.

In this case one of the equations is already solved for one of the variables (y):

y = -2x + 1

So the next step is to plug this in the other equation wich is:

4x + 2y = -3

So we will have

4x + 2(-2x + 1) = -3

solving the parenthesis:

4x-4x -2= -3

-2= -3

wich is not a valid answer, so the system of equations has no solution.

True [87]3 years ago
6 0
4x+2(-2x+1)=-3
4x-4x+2=-3
2=-3 is not a true statement.

The answer is no solution
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3. First you should identify which line corresponds to which equation.

x + 2y = -8   ⇒   y = -x/2 - 4

is the line with slope -1/2 and intercept (0, -4), so the first inequality refers to the lower line in the graph.

For the inequality itself, the solution set that satisfies it is either the region above or below it. To decide which, pick any point in the plane and plug its coordinates into the inequality. The origin is a natural choice, since it's not on the line and working with 0s is easy.

In the first inequality, we have

x = 0 and y = 0   ⇒   0 + 2•0 = 0 < -8

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In the second inequality,

x = 0 and y = 0   ⇒   2•0 + 0 = 0 ≥ -1

which is true. This means the region containing (0, 0) above the upper line solves the second inequality.

The solution to the system of inequalities is then the intersection of these two regions. (See attached; I've labeled the solution to the first inequality in blue, the solution to the second one in red, and the solution to both in green.)

All this work is kind of overkill for this particular question, though. All you really need to do is check if the given point satisfies the inequalities:

• (-5, 5) :

x = -5 and y = 5   ⇒   -5 + 2•5 = 5 < -8   ⇒   NO

• (2, -5) :

x = 2 and y = -5   ⇒   -2 + 2•5 = 8 < -8   ⇒   NO

• (-4, -6) :

x = -4 and y = -6   ⇒   -4 + 2•(-6) = -16 < -8   ⇒   MAYBE

x = -4 and y = -6   ⇒   2•(-4) + (-6) = -14 < -8   ⇒   YES

• (5, -7) :

x = 5 and y = -7   ⇒   5 + 2•(-7) = -9 < -8   ⇒   MAYBE

x = 5 and y = -7   ⇒   2•5 + (-7) = 3 < -8   ⇒   NO

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This means Regions II and III solve the first inequality.

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has positive slope. This leaves D.

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