2×2= Have a nice night.

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

When 6x² - 4x+3 is subtracted from 3x²–2x+3, the result is

mr_godi [17]

Let's subtract then: 3x2 - 2x + 3 - (6x2 - 4x + 3)

taking out of the bracket with a changed sign: (there is a minus in front of the bracket)

3x2 - 2x + 3 - 6x2 + 4x - 3
let's reshuffle them so that similar terms are together:
3x2 - 6x2 - 2x + 4x + 3 - 3

Adding up similar terms:

-3x2 + 2x - that's our option 2!

4 0

3 years ago

Ella planted of the garden in the morning. She planted of the garden in the afternoon.

velikii [3]

There correct answer is B!

4 0

3 years ago

Help please (will chose brainliest).

lara [203]

Answers with Explanation.

i. If we raise a number to an exponent of 1, we get the same number.

${10}^{1} = 10$

ii. If we raise 10 to an exponent of 2, it means we multiply 10 by itself two times.

${10}^{2} = 10 \times 10 = 100$

iii. If we raise 10 to an exponent of 3, it means we multiply 10 by itself three times.

${10}^{3} = 10 \times {10}^{2} = 10 \times 100 = 1000$

iv. If we raise 10 to an exponent of 4, it means we multiply 10 by itself four times.

${10}^{4} = 10 \times {10}^{3} = 10 \times 1000 = 10000$

v. If we raise 10 to an exponent of 5, it means we multiply 10 by itself five times.

${10}^{5} = 10 \times {10}^{4} = 10 \times 10000 = 100000$

${10}^{5} = 100000$

vi. Recall that,

${a}^{ - m} = \frac{1}{ {a}^{m} }$
We apply this law of exponents to obtain,

${10}^{ - 2} = \frac{1}{{10}^{2} } = \frac{1}{100}$

vii. We apply
${a}^{ - m} = \frac{1}{ {a}^{m} }$
again to obtain,

${10}^{ - 3} = \frac{1}{ {10}^{3} } = \frac{1}{1000}$

5 0

3 years ago

A gift box is the shape of a rectangular prism. The box has a length of 24 centimeters, a width of 10 centimeters, and a height

Kamila [148]

Volume (V) is (=) Length (L) times (x) Width (W) times (x) Height (H) so V = L x V x H.

Add the variables to the equation.
V = 24 x 10 x 13

Solve
V = 3120

So the volume of the gift box is 3120 cm

6 0

3 years ago