![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
Given: The equation set y = 2x + 3 and y = 4x + 7
\n" ); document.write( ".
\n" ); document.write( "You are asked to solve this set by substitution. Note that the first equation defines
\n" ); document.write( "the value of y in terms of x. Therefore, you can use the right side of this equation
\n" ); document.write( "(2x + 3) as a substitution for y in the second equation. When you substitute 2x +3 for y
\n" ); document.write( "in the second equation, the result is:
\n" ); document.write( ".
\n" ); document.write( "2x + 3 = 4x + 7
\n" ); document.write( ".
\n" ); document.write( "Let's set the goal of getting all the terms that contain x isolated on the left side of
\n" ); document.write( "the equal sign and all the constants by themselves on the right side. Begin by getting rid
\n" ); document.write( "of the +3 on the left side by subtracting 3 from the left side. But if you subtract
\n" ); document.write( "3 from the left side you must also subtract 3 from the right side. These subtractions
\n" ); document.write( "result in the following sequence:
\n" ); document.write( ".
\n" ); document.write( "2x + 3 - 3 = 4x + 7 - 3
\n" ); document.write( ".
\n" ); document.write( "Combining numbers on the left side and on the right side simplifies the equation to:
\n" ); document.write( ".
\n" ); document.write( "2x = 4x + 4
\n" ); document.write( ".
\n" ); document.write( "Now, in a similar fashion, let's get rid of the 4x on the right side by subtracting
\n" ); document.write( "4x from the right side. When we do this subtraction, to keep the equation in balance
\n" ); document.write( "we must also subtract 4x from the left side. This results in:
\n" ); document.write( ".
\n" ); document.write( "2x - 4x = 4x - 4x + 4
\n" ); document.write( ".
\n" ); document.write( "On both sides of the equation combine terms containing x to get:
\n" ); document.write( ".
\n" ); document.write( "-2x = 4
\n" ); document.write( ".
\n" ); document.write( "Finally, solve for x by dividing both sides of the equation by -2 because -2 is the multiplier
\n" ); document.write( "of x. This results in:
\n" ); document.write( ".
\n" ); document.write( "x = 4/-2 = -2
\n" ); document.write( ".
\n" ); document.write( "So now that we know x = -2, we can return to either one of the original equations
\n" ); document.write( "in the equation set and substitute -2 for x. Then we can solve for y. Let's return
\n" ); document.write( "to the first equation and substitute -2 for x. This begins with:
\n" ); document.write( ".
\n" ); document.write( "y = 2x + 3
\n" ); document.write( ".
\n" ); document.write( "Then substituting -2 for x gives:
\n" ); document.write( ".
\n" ); document.write( "y = 2*(-2) + 3 = -4 + 3 = -1
\n" ); document.write( ".
\n" ); document.write( "In summary, our answers for the equation set is x = -2 and y = -1. Keep in mind what this
\n" ); document.write( "means ... both equations are satisfied by setting x to -2 and y to -1. It also means that
\n" ); document.write( "the point (-2,-1) is the point at which the graphs of the two equations intersect.
\n" ); document.write( ".
\n" ); document.write( "Hope this helps you to understand how to solve for the variables in the equation set by
\n" ); document.write( "using the process of substitution. \n" ); document.write( "