Stephen W. answered • 06/07/14

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Online answer to Geometry, Algebra 1-2, English and more! Here to help

x= .25

y= .50

Change back from $20 = 10.75

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x + y = 30

.25x + .50y = 10.75

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Substitution? Elimination? Graphing?

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Substitution:

x + y = 30

.25x + .5y = 10.75

Pick one of the equations, and solve for the variable of your choice:

y = 30 - x

Substitute this into the other equation for the variable you solved:

.25x + .5(30-x) = 10.75

Distribute:

.25x + 15 - .5x = 10.75

Combine like terms:

-.25x + 15 = 10.75

Subtract 15 from both sides:

-.25x = -4.25

Divide both sides by -.25:

x = 17

After all of that, we now have a number value for one of our variables, in this case, 'x'. Now we pick one of the original equations, and plug 17 into the equation for 'x'. I chose the first equation:

17 + y = 30

Subtract 17 from both sides:

y = 13

The solution for the problem is (17, 13). On a graph, this is the coordinate pair for the exact point where the two lines cross each other. Check by putting 'x' and 'y' back into each equation and solve that side of the equation. If it equals the number given, then it is valid.

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I hope this was helpful! Going forward, it is important to note which method the teacher wants you to use to solve, or if it even matters. Thanks!