## solving system of equations: 3m + 2p = 1.8, 4m + 6p = 2.9

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
mathphobic1
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### solving system of equations: 3m + 2p = 1.8, 4m + 6p = 2.9

3m+2p=1.80

4m+6p=2.90

solve for m and p

jaybird0827
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### Re: solving system of equations: 3m + 2p = 1.8, 4m + 6p = 2.9

mathphobic1 wrote:3m+2p=1.80

4m+6p=2.90

solve for m and p

$3m\,+\,2p\,=\,1.80$
$4m\,+\,6p\,=\,2.90$

Solving systems of equations by substitution : http://www.purplemath.com/modules/systlin4.htm
Solving systems of equations by addition/elimination : http://www.purplemath.com/modules/systlin5.htm

Since none of the $m$ or $p$ terms has a coefficient of $1$, the addition method has the advantage.

Notice that if you were to multiply the top equation through by $3$, that would make it easy to eliminate $p$ and solve for $m$.

1.) Multiply both sides of the top equation by $3$.
2.) Multiply both sides of the bottom equation by $-1$.
3.) Add together. The $p$ terms drop out.
4.) Solve the resulting equation for $m$.
5.) Take the value of m that you got in step 4, plug it in for $m$ in the first equation, and solve the resulting equation for $p$.
6.) Check both values from steps 4 and 5 into both original equations.
7.) Answer $m\,=$ (whatever m equals), $p\,=$ (whatever p equals).

Please follow the above steps to complete the solution.
If you get stuck, please reply showing the steps that you followed and what you got for each step.

pzrose
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Joined: Wed Jul 15, 2009 11:41 am
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### Re: solving system of equations: 3m + 2p = 1.8, 4m + 6p = 2.9

3m + 2p = 1.8 (equation 1
4m + 6p = 2.9 (equation 2

multiply equation 1 by 6 and equation 2 by 6
6x3m + 6x2p = 6x1.8
2x4m +2x6p = 2x2.9

18m+12p = 10.8 (equation 3
8m+12p = 5.8 (equation 4

equation 3 minus equation 4

10m+0=5 then divide 10m=5 by 10 to make m the subject

therefore m=1/2 or 0.5

we then take equation 4 and place the result for m (m=1/2 or 0.5

so we have 8(1/2)+12p=5.8

divide through by 2 so we have 2(8(1/2))+2x12p=2x5.8 to give us

8+24p=11.6 we now make p the subject

24p=11.6 - 8

24p=3.6 divide through by 24 to give us

therefore p=0.15