Solved on Oct 31, 2023

Solve the system of linear equations: $8m + 10n = 17$ and $3m + 7n - 8 = 0$ .

STEP 1

Assumptions1. We have two simultaneous linear equations in two variables, m and n. . The equations are -8m +10n =17 -3m +7n -8 =0

STEP 2

We can rewrite the second equation to make it in the same format as the first equation.
$m +7n =8$

STEP 3

Now, we have two equations $\begin{aligned} 8 m+10 n & =17 \\ 3 m+7 n & =8\end{aligned}$

STEP 4

To solve these equations, we can use the method of substitution or elimination. Here, we will use the method of elimination. To do this, we need to make the coefficients of m or n the same in both equations. Let's multiply the first equation by3 and the second equation by8 to make the coefficients of m the same.
$\begin{aligned} 24 m+30 n & =51 \\ 24 m+56 n & =64\end{aligned}$

STEP 5

Now, we subtract the second equation from the first to eliminate m.
$\begin{aligned} (24 m+30 n) - (24 m+56 n) & =(51 -64) \\ -26 n & =-13\end{aligned}$

STEP 6

We can now solve for n by dividing both sides of the equation by -26.
$n = -13 / -26 =0.5$

STEP 7

Now that we have the value of n, we can substitute it into the first equation to solve for m.
$m +10(0.5) =17$

STEP 8

implify the equation.
$8m +5 =17$

STEP 9

Subtract5 from both sides of the equation to isolate m.
$8m =17 -5$

STEP 10

implify the equation.
$8m =12$

STEP 11

Finally, solve for m by dividing both sides of the equation by8.
$m = /8 =.5$ So, the solution to the simultaneous equations is m =.5 and n =0.5.

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Solve the system of linear equations: $8m + 10n = 17$ and $3m + 7n - 8 = 0$ .

STEP 1

Assumptions1. We have two simultaneous linear equations in two variables, m and n. . The equations are -8m +10n =17 -3m +7n -8 =0

STEP 2

We can rewrite the second equation to make it in the same format as the first equation.
$m +7n =8$

STEP 3

Now, we have two equations $\begin{aligned} 8 m+10 n & =17 \\ 3 m+7 n & =8\end{aligned}$

STEP 4

STEP 5

Now, we subtract the second equation from the first to eliminate m.
$\begin{aligned} (24 m+30 n) - (24 m+56 n) & =(51 -64) \\ -26 n & =-13\end{aligned}$

STEP 6

We can now solve for n by dividing both sides of the equation by -26.
$n = -13 / -26 =0.5$

STEP 7

Now that we have the value of n, we can substitute it into the first equation to solve for m.
$m +10(0.5) =17$

STEP 8

implify the equation.
$8m +5 =17$

STEP 9

Subtract5 from both sides of the equation to isolate m.
$8m =17 -5$

STEP 10

implify the equation.
$8m =12$

STEP 11

Finally, solve for m by dividing both sides of the equation by8.
$m = /8 =.5$ So, the solution to the simultaneous equations is m =.5 and n =0.5.

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Solve the system of linear equations: 8m+10n=178m + 10n = 178m+10n=17 and 3m+7n−8=03m + 7n - 8 = 03m+7n−8=0.

STEP 1

Assumptions1. We have two simultaneous linear equations in two variables, m and n. . The equations are -8m +10n =17 -3m +7n -8 =0

STEP 2

We can rewrite the second equation to make it in the same format as the first equation.m+7n=8m +7n =8m+7n=8

STEP 3

Now, we have two equations8m+10n=173m+7n=8\begin{aligned} 8 m+10 n & =17 \\ 3 m+7 n & =8\end{aligned} 8m+10n3m+7n​=17=8​

STEP 4

STEP 5

Now, we subtract the second equation from the first to eliminate m.(24m+30n)−(24m+56n)=(51−64)−26n=−13\begin{aligned} (24 m+30 n) - (24 m+56 n) & =(51 -64) \\ -26 n & =-13\end{aligned} (24m+30n)−(24m+56n)−26n​=(51−64)=−13​

STEP 6

We can now solve for n by dividing both sides of the equation by -26.n=−13/−26=0.5n = -13 / -26 =0.5n=−13/−26=0.5

STEP 7

Now that we have the value of n, we can substitute it into the first equation to solve for m.m+10(0.5)=17m +10(0.5) =17m+10(0.5)=17

STEP 8

implify the equation.8m+5=178m +5 =178m+5=17

STEP 9

Subtract5 from both sides of the equation to isolate m.8m=17−58m =17 -58m=17−5

STEP 10

implify the equation.8m=128m =128m=12

STEP 11

Finally, solve for m by dividing both sides of the equation by8.m=/8=.5m = /8 =.5m=/8=.5So, the solution to the simultaneous equations is m =.5 and n =0.5.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the system of linear equations: $8m + 10n = 17$ and $3m + 7n - 8 = 0$ .

We can rewrite the second equation to make it in the same format as the first equation.
$m +7n =8$

Now, we have two equations $\begin{aligned} 8 m+10 n & =17 \\ 3 m+7 n & =8\end{aligned}$

Now, we subtract the second equation from the first to eliminate m.
$\begin{aligned} (24 m+30 n) - (24 m+56 n) & =(51 -64) \\ -26 n & =-13\end{aligned}$

We can now solve for n by dividing both sides of the equation by -26.
$n = -13 / -26 =0.5$

Now that we have the value of n, we can substitute it into the first equation to solve for m.
$m +10(0.5) =17$

implify the equation.
$8m +5 =17$

Subtract5 from both sides of the equation to isolate m.
$8m =17 -5$

implify the equation.
$8m =12$

Finally, solve for m by dividing both sides of the equation by8.
$m = /8 =.5$ So, the solution to the simultaneous equations is m =.5 and n =0.5.