document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971554>Question 971554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello tutor, I really need your help to solve this question please.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve the system: y = x^2 + 7, y = 4x + 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593981 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593981\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  y = x^2 + 7, y = 4x + 3<BR>\n" );
document.write( "</pre><BR>\n" );
document.write( "Since y equals to both x^2 + 7 and to 4x + 3, set them equal to each other:\r<BR>\n" );
document.write( "\n" );
document.write( " x^2 + 7 = 4x + 3\r<BR>\n" );
document.write( "\n" );
document.write( "Get 0 on the right by subtracting the right side from both sides:\r<BR>\n" );
document.write( "\n" );
document.write( " x^2 - 4x + 4 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "Factor the left side:\r<BR>\n" );
document.write( "\n" );
document.write( "(x - 2)(x - 2) = 0\r<BR>\n" );
document.write( "\n" );
document.write( "x - 2 = 0;  x - 2 = 0<BR>\n" );
document.write( "    x = 2       x = 2\r<BR>\n" );
document.write( "\n" );
document.write( "There is one solution since both came out the same.\r<BR>\n" );
document.write( "\n" );
document.write( "Find y by substituting in either of the two original equations:\r<BR>\n" );
document.write( "\n" );
document.write( " y = 4x + 3<BR>\n" );
document.write( " y = 4(2) + 3<BR>\n" );
document.write( " y = 8 + 3<BR>\n" );
document.write( " y = 11\r<BR>\n" );
document.write( "\n" );
document.write( "So the solution is (x,y) = (2,11), which means that the graphs of\r<BR>\n" );
document.write( "\n" );
document.write( " y = x^2 + 7 and y = 4x + 3\r<BR>\n" );
document.write( "\n" );
document.write( "intersect at the point (2,11)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-13%2C13%2C-5%2C21%2Cx%5E2%2B7%2C4x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-13%2C13%2C-5%2C21%2Cx%5E2%2B7%2C4x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Edwin</pre> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );