Question 220150
(Note: The solution provided by someone else did not use the substitution method.)
The substitution method:<ol><li>Solve one equation (either one) for one of the variables (either one). So choose that variable and the equation that makes this step easiest.</li><li>Substitute into the <b>other</b> equation for that variable. This changes the equation into a one-variable equation.</li><li>Solve the one-variable equation for that variable.</li><li>Take the value for this variable and substitute it back into one of the original equations (either one). Once again a one-variable equation results.</li><li>Solve this one variable equation for the second variable</li></ol>
1. Solve an equation for one of the variables. The "easy" systems for the substitution method are the ones where a variable has a coefficient of 1 (or -1). Unfortunately this system is not an "easy" one. Since I prefer positives I'll solve the second equation for y:
5x - 2y = -12
Add 2y to both sides:
5x = 2y - 12
Add 12 to both side:
5x + 12 = 2y
Multiply both sides by 1/2 (or divide by two):
{{{(5/2)x + 6 = y}}}<br>
2. Substitute into the other equation:
2x + 3y = -1
{{{2x + 3((5/2)x + 6) = -1}}}
<br>
3. Solve this equation.
Simplify.
{{{2x + (15/2)x + 18 = -1}}}
{{{(4/2)x + (15/2)x + 18 = -1}}}
{{{(19/2)x + 18 = -1}}}
Subtract 18 from each side:
{{{(19/2)x = -19}}}
Multiply by 2/19 (or divide by 19/2):
{{{x = -2}}}<br>
4. Substitute this solution back into one of the original equations:
2x + 3y = -1
2(-2) + 3y = -1<br>
5. Solve this equation.
Simplify.
-4 + 3y = -1
Add 4 to both sides:
3y = 3
Multiply both sides by 1/3 (or divide by 3):
y = 1<br>
So the solution is the point (-2, 1)