Solving a system of linear equations

Juan buys peaches and grapefruit at the store.  He writes the equations shown to model the relationship between the number of pounds of peaches, p, and the number of pounds of grapefruit, g, that he buys.

​p + g = 2.5
1.58p + 1.09g = 3.46

What is the total number of pounds of peaches and grapefruit that Juan buys?

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​p + g = 2.5
1.58p + 1.09g = 3.46

-1.58p - 1.58g = -3.95   {multiplied first equation by -1.58}
1.58p + 1.09g = 3.46   {second equation stays the same}
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             -0.49g = -0.49   {added the two equations together}
                      g = 1   {divided each side by -0.49}

p + g = 2.5   {first original equation}
p + 1 = 2.5   {substituted 1, in for g, into first original equation}
      -1    -1
p = 1.5   {subtracted 1 from each side}

1.5 pounds of peaches
1 pound of grapefruit

=  2.5 pounds of peaches and grapefruit

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