Question 557977
A simple example of substitution is:
(1) {{{ x + y = 5 }}}
(2) {{{ y = 3 + x }}}
Substitute (2) into (1)
You can do this because {{{ y }}} appears
in both equations
(1) with the substitution is:
(1) {{{ x + ( 3 + x ) = 5 }}}
(1) {{{ 2x + 3 = 5 }}}
(1) {{{ 2x = 2 }}}
(1) {{{ x = 1 }}}
and, since
(2) {{{ y = 3 + x }}}
(2) {{{ y = 3 + 1 }}}
(2) {{{ y = 4 }}}
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Here's your problem:
(1) {{{ x + y = 4 }}}
(2) {{{ y = 3x }}}
I will substitute (2) into (1)
(1) {{{ x + ( 3x ) = 4 }}}
(1) {{{ 4x = 4 }}}
(1) {{{ x = 1 }}}
and, since
(2) {{{ y = 3x }}}
(2) {{{ y = 3*1 }}}
(2) {{{ y = 3 }}}
So, the solution is the point (1,3)
Here's a plot of the lines
(1) {{{ x + y = 4 }}}
(2) {{{ y = 3x }}}
{{{ graph( 400, 400, -6, 6, -6, 6, -x + 4, 3x ) }}}