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1 year ago

How many solutions does the system have? Y= 4x8 4y = 4x - 8

Mathematics

1 answer:

statuscvo [17]1 year ago

7 0

The number of solutions to the system is 1

<h3>What is a linear equation?</h3>

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

<h3>How to determine the number of solution to the system?</h3>

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y = 4x + 8

4y = 4x - 8

Substitute y = 4x + 8 in 4y = 4x - 8

4(4x + 8) = 4x - 8

Expand the equation

16x + 32 = 4x - 8

Evaluate the like terms

12x = - 40

Divide by 12

x = -10/3

The above means that the number of solutions to the system is 1

Read more about system of linear equations at

brainly.com/question/14323743

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<h3>Inequalities</h3>

Inequalities is a mathematic expression that do not present equalitiy between both sides. It is represented by symbols: <, ≤, > and ≥.

For solving this exercise, firstly, you should solve the inequalities identified by letters: H, W, M, Y and C. After that, you should relate yours anwers with the options given for the exercise.

Inequality H

$-11x-4 > -15\\ \\ -11x > -15+4\\ \\ -11x > -11\; *(-1)\\ \\ 11x < 11\\ \\ x < 1$

Therefore, you should connect H with x<1.

Inequality W

$32 > -16x\\ \\ Rewriting \\ \\ -16x < 32 \\ \\ -16x < 32\; *(-1)\\ \\ 16x > -32\\ \\ x > \frac{-32}{16} \\ \\ x > -2$

Therefore, you should connect W with x>-2.

Inequality M

$3+x\leq -9\\ \\ x\leq -9-3\\ \\ x\leq -12$

Therefore, you should connect M with x≤-12.

Inequality Y

$-7x+7\leq -56\\ \\-7x\leq -56-7\\ \\ -7x\leq -63\\ \\ -7x\leq -63\; *(-1)\\ \\ 7x\geq 63\\ \\ x\geq \frac{63}{7} \\ \\ x\geq 9$

Therefore, you should connect Y with x≥9.

Inequality C

$-20\geq -5x+15\\ \\Rewriting\\ \\ 5x+15\leq -20\\ \\ -5x\leq -20-15\\ \\ -5x\leq -35\\ \\-5x\leq -35\; *(-1)\\ \\ 5x\geq 35\\ \\ x\geq \frac{35}{5} \\ \\ x\geq 7$

Therefore, you should connect C with x≥7.

Thus, the sequence is:

M - $x\leq -12$

C - $x\geq 7$

Y- $x\geq 9$

H- $x < 1$

W- $x > -2$