document.write( "Question 127303: What is the solution to the sysytem of equations y=2x and y=-x+3?\r
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Algebra.Com's Answer #93257 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Start with the given system\r
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\n" ); document.write( "\n" ); document.write( "\"-x%2B3=2x\" Plug in \"y=-x%2B3\" into the first equation. In other words, replace each \"y\" with \"-x%2B3\". Notice we've eliminated the \"y\" variables. So we now have a simple equation with one unknown.\r
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\n" ); document.write( "\n" ); document.write( "\"-x%2B3=2x\" Distribute\r
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\n" ); document.write( "\n" ); document.write( "\"-x=2x-3\"Subtract 3 from both sides\r
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\n" ); document.write( "\n" ); document.write( "\"-x-2x=-3\" Subtract 2x from both sides\r
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\n" ); document.write( "\n" ); document.write( "\"-3x=-3\" Combine like terms on the left side\r
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\n" ); document.write( "\n" ); document.write( "\"x=%28-3%29%2F%28-3%29\" Divide both sides by -3 to isolate x\r
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\n" ); document.write( "\n" ); document.write( "\"x=1\" Divide\r
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\n" ); document.write( "\n" ); document.write( "Now that we know that \"x=1\", we can plug this into \"y=-x%2B3\" to find \"y\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%281%29%2B3\" Substitute \"1\" for each \"x\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=2\" Simplify\r
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\n" ); document.write( "\n" ); document.write( "So our answer is \"x=1\" and \"y=2\" which also looks like \r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.\r
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\n" ); document.write( "\n" ); document.write( "\"+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+2x%2C+-x%2B3%29+\" Graph of \"y=2x\" (red) and \"y=-x%2B3\" (green)\r
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