Question 734890
Substitution means that your first step is solving for one variable in one of the equations. For example
{{{y-5x=-2}}} --> {{{y=5x-2}}}
Note: Look for a variable that has no visible coefficient. In this case, the coefficient of {{{y}}} in {{{y-5x=-2}}} is an invisible number 1.
 
The second step when using substitution is to substitute the expression found for the variable in the other equation.
In this case, since we found that {{{y=5x-2}}}, we write (5x-2) instead of {{{y}}} in {{{3x-7y=22}}} to get
{{{3x-7(5x-2)=22}}}
No we use the distributive property to transform that into
{{{3x-7*(5x)-7*(-2)=22}}} and simplify to {{{3x-35x+14=22}}} and {{{-32x+14=22}}}
Then we solve {{{-32x+14=22}}}
{{{-32x+14=22}}} --> {{{-32x=22}-14}} --> {{{-32x=8}}} --> {{{x=8/(-32)}}} --> {{{highlight(x=-1/4)}}}
 
As a final step, we substitute {{{-1/4}}} for {{{x}}} somewhere to find {{{y}}}.
It may be easiest to use {{{y=5x-2}}}. Substituting we get
{{{y=5(-1/4)-2}}}--> {{{y=-5/4-2}}} --> {{{y=-5/4-8/4}}} --> {{{highlight(y=-13/4)}}}
 
NOTE: If you cannot find a variable with no visible coefficient, substitution will get cumbersome, as you would be working with fractions a lot. In that case, it is better to use a different method.