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3 years ago

What is the solution to 3x -2y =1 and 4y = 7 + 3x

Mathematics

1 answer:

Delvig [45]3 years ago

8 0

Given.

$3x-2y=1$ (1)

$4y=7+3x$ (2)

Re-arrange equation (2)

$(4y=7+3x)-4y$

$0=-4y+3x+7$

$(0=-4y+3x+7)-7$

$-7=-4y+3x$

Multiply equation (2) by -1

$-1(3x-4y=-7)$

$-3x+4y=7$ (3)

Combine like terms and solve.

$3x-3x-2y+4y=1+7$

$2y=8$

Divide by (2y) and solve for (y).

$\frac{2y}{2}=\frac{8}{2}$

$y=4$

Substitute (y) for equation (1).

$3x-2y=1$

$3x-2(4)=1$

$3x-8=1$

Add (8) to both sides.

$(3x-8)+8=(1)+8$

$3x=9$

Divide by (3).

$\frac{3x}{3}=\frac{9}{3}$

$x=3$

Check your work.

$3x-2y=1$

$3(3)-2(4)=1$

$9-8=1$

$1=1$

$4y=7+3x$

$4(4)=7+3(3)$

$16=7+9$

$16=16$

Your answers is $x=3$ and $y=4$

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erik [133]

Answer:

25 girls

Step-by-step explanation:

Let

x denote number of boys

and

y denote number of girls

According to the statement that total 45 people came,

x+y = 45 => Eqn 1

And total paid amount was 175

So,

5x + 3y = 175 => Eqn 2

For solving, We will use the substitution method

So, from eqn 1

x = 45-y

Putting value of x in eqn 2

5(45-y) +3y = 175

225 - 5y + 3y = 175

-2y+225 = 175

-2y = 175-225

-2y = -50

2y = 50

y = 25

Putting y =25 in eqn 1

x+25 = 45

x = 45 - 25

x = 20

As y= 25

So, 25 girls came to the dance ..

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3 years ago

Find the value of x using segment addition.

kolbaska11 [484]

You combine both 2x-12 and x+2 and 11 which makes the equation

2x-12+x+2= 11

The you get your answer which is

X=7

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3 years ago

According to the Fundamental Theorem of Algebra, the graph of f(x) = x2 - 4x + 3, has roots. From the graph we can see that it h

andreyandreev [35.5K]

Answer:

The graph $f(x)=x^2-4x+3$ has two zeros namely 3 and 1.

Step-by-step explanation:

Consider the given equation of graph $f(x)=x^2-4x+3$

According to the Fundamental Theorem of Algebra

For a given polynomial of degree n can have a maximum of n roots.

Thus, for the given equation $f(x)=x^2-4x+3$ the degree of polynomial is 2 , thus the function can have maximum of 2 roots.

We know at roots the value of function is 0 that is f(x) = 0,

Substitute f(x) = 0 , we get, $f(x)=x^2-4x+3=0$

This is a quadratic equation, $x^2-4x+3=0$

We first solve it manually and then check by plotting graph.

Quadratic equation can be solved using middle term splitting method,

here, -4x can be written as -x-3x,

$x^2-4x+3=0 \Rightarrow x^2-x-3x+3=0$

$\Rightarrow x(x-1)-3(x-1)=0$

$\Rightarrow (x-3)(x-1)=0$

Using zero product property, $a\cdot b=0 \Rightarrow a=0\ or \ b=0$

$\Rightarrow (x-3)=0$ or $\Rightarrow (x-1)=0$

$\Rightarrow x=3$ or $\Rightarrow x=1$

Thus, the two zero of f(x) are 3 and 1.

We can also see on graph attached below that the graph $f(x)=x^2-4x+3$ has two zeros namely 3 and 1.

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3 years ago

Michael puts $800 into a savings account. The account earns 2% simple interest. How much interest will he earn in 6 months?

expeople1 [14]

Answer:

he earned 8 dollars in interest

Step-by-step explanation:

800(1+(.02)(.5))

hopefully im correct

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3 years ago

A transversal intersects two parallel lines. The measures of a pair of alternate interior angles are 5v and 2w. The measures of

Nataly_w [17]

Answer:

The value of v is 6° and the value of w is 15°

Step-by-step explanation:

we know that

When parallel lines are cut by a transversal line, the same-side exterior angles are supplementary and each pair of alternate interior angles is equal in measure

5v=2w -----> equation A

10w+5v=180 ----> equation B

substitute equation A in equation B and solve for w

10w+(2w)=180

12w=180

w=15°

Find the value of v

5v=2w -----> v=2w/5

v=2(15)/5=6°

therefore

The value of v is 6° and the value of w is 15°

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3 years ago