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How do I solve 2m + n = 2 and 3m - 2n = 3 using substitution?

Leona [35]

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

Solve 2m + n = 2 and 3m - 2n = 3 using substitution.

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

We can use the substitution method to solve linear equations of this form. Let's solve for m & n.

$\left. \begin{array} { l } { 2 m + n = 2 } \\ { 3 m - 2 n = 3 } \end{array} \right.$

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.

$2m+n=2, \: 3m-2n=3$

Choose one of the equations and solve it for m by isolating m on the left-hand side of the equal sign.

$2m+n=2$

Subtract n from both sides of the equation.

$2m=-n+2$

Divide both sides by 2.

$m=\frac{1}{2}\left(-n+2\right) \\$

Multiply 1/2 times -n+2.

$m=-\frac{1}{2}n+1 \\$

Substitute $-\frac{n}{2}+1\\$ for m in the other equation, 3m-2n=3.

$3\left(-\frac{1}{2}n+1\right)-2n=3 \\$

Multiply 3 times $-\frac{n}{2}+1\\$ .

$-\frac{3}{2}n+3-2n=3 \\$

Add $-\frac{3n}{2}\\$ to -2n.

$-\frac{7}{2}n+3=3 \\$

Subtract 3 from both sides of the equation.

$-\frac{7}{2}n=0 \\$

Divide both sides of the equation by $-\frac{7}{2}\\$ , which is the same as multiplying both sides by the reciprocal of the fraction.

$\large \underline{\underline{ \bf \: n=0 }}$

Substitute 0 for n in $m=-\frac{1}{2}n+1\\$ . Because the resulting equation contains only one variable, you can solve for m directly.

$\large \underline{ \underline{\bf \: m=1 }}$

The system is now solved.

$\huge \boxed{ \boxed{ \bf \: m=1, \: n=0 }}$

4 0

2 years ago

What is sum of all palindromic numbers from 1 to 100

Gekata [30.6K]

Answer:

540

Step-by-step explanation:

0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99

7 0

2 years ago

Read 2 more answers

Answer pleaseeee??? Thanks

inessss [21]

Answer:

True!

Step-by-step explanation:

3(10) - 9

30 - 9

21

5 0

2 years ago

Read 2 more answers

X^2- 6x - 7 = 0 can someone help me solve this by completing the square

Crazy boy [7]

I think it’s X=-3+(the square root of 2)

3 0

3 years ago

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A rectanglar swimming pool is three times as long as it is wide. If the perimeter of the soccer feild is 300 yards, what are the

fredd [130]

Answer:

The dimension of the rectangular pool is $112.5\times 37.5$

Step-by-step explanation:

Given : A rectangular swimming pool is three times as long as it is wide. If the perimeter of the soccer field is 300 yards.

To find : What are the dimensions?

Solution :

Let the width of the rectangular pool be 'x'.

A rectangular swimming pool is three times as long as it is wide.

The length of the pool be '3x'

The perimeter of the rectangular swimming pool is $P=2(l+w)$

The perimeter of the soccer field is 300 yards.

Substitute the value in the formula,

$300=2(3x+x)$

$300=2\times 4x$

$300=8x$

$x=\frac{300}{8}$

$x=37.5$

The width of the pool is x=37.5 unit

The length of the pool is $3x=3(37.5)=112.5$

Therefore, The dimension of the rectangular pool is $112.5\times 37.5$

4 0

3 years ago