Which graph best represents the equation 12x+6y=0?

Solve the following using Substitution method 2x – 5y = -13 3x + 4y = 15

Digiron [165]

$\huge \boxed{\mathfrak{Question} \downarrow}$

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\left. \begin{array} { l } { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$2x-5y=-13, \: 3x+4y=15$

Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

$2x-5y=-13$

Add 5y to both sides of the equation.

$2x=5y-13$

Divide both sides by 2.

$x=\frac{1}{2}\left(5y-13\right) \\$

Multiply $\frac{1}{2}\\$ times 5y - 13.

$x=\frac{5}{2}y-\frac{13}{2} \\$

Substitute $\frac{5y-13}{2}\\$ for x in the other equation, 3x + 4y = 15.

$3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15 \\$

Multiply 3 times $\frac{5y-13}{2}\\$ .

$\frac{15}{2}y-\frac{39}{2}+4y=15 \\$

Add $\frac{15y}{2} \\$ to 4y.

$\frac{23}{2}y-\frac{39}{2}=15 \\$

Add $\frac{39}{2}\\$ to both sides of the equation.

$\frac{23}{2}y=\frac{69}{2} \\$

Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

$\large \underline{ \underline{ \sf \: y=3 }}$

Substitute 3 for y in $x=\frac{5}{2}y-\frac{13}{2}\\$ . Because the resulting equation contains only one variable, you can solve for x directly.

$x=\frac{5}{2}\times 3-\frac{13}{2} \\$

Multiply 5/2 times 3.

$x=\frac{15-13}{2} \\$

Add $-\frac{13}{2}\\$ to $\frac{15}{2}\\$ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

$\large\underline{ \underline{ \sf \: x=1 }}$

The system is now solved. The value of x & y will be 1 & 3 respectively.

$\huge\boxed{ \boxed{\bf \: x=1, \: y=3 }}$

8 0

2 years ago

Which expression is equivalent to this polynomial? 6x2 + 10x − 56=

hammer [34]

2nd one maybe I’m not to sure srry

4 0

3 years ago

Read 2 more answers

Please choose answer choice a,b,c or d

dmitriy555 [2]

Answer:

A. -4

Step-by-step explanation:

Slope is rise over run, or y2-y1 / x2-x1.

$\frac{y2-y1}{x2-x1} = \frac{-4-8}{2--1} =\frac{-12}{3} = -4$

The slope is A. -4.

Let's see--does that make sense? A slope of four would be pretty steep, and that matches the graph. It also should be negative because the line goes down and to the right, not up and to the right, so -4 makes sense!

4 0

3 years ago

JULIE HAS 10 YARDS OF RIBBON. SHE DIVDES THE RIBBON INTO 3 EQUAL PIECES AND USES 2 OF THE PIECES ON GIFTS. HOW MUCH RIBBON DOES

Aliun [14]

Answer:

6.66 yards of ribbon.

Step-by-step explanation:

If she has 10 yards of ribbon and divides it equally into three parts, those 3 parts would each be 3.33 yards long or 3 (1/3) yards long.

If she uses two of those parts on gifts, then she would use 3.33 x 2 or 6.66 yards of ribbon.

8 0

3 years ago

According to the two-way table, how many people chose Decision Y?

larisa [96]

Easy peasy

so you just add the people in collumn 'decision y' and get the answer

105+67=172
answer is 172 chose decision y

7 0

3 years ago