# Solving Systems Using the Substitution Method

2x+3y=10
y=-x+2

### Comments for Solving Systems Using the Substitution Method

Average Rating     Apr 18, 2010 Rating     Solving Systems Using the Substitution Method by: Karin This problem is set up very nicely for using the substitution method. The second equation is already solved for y, so we can substitute -x + 2 into the first equation for y. Here is a step-by-step explanation. 2x + 3y = 10 y = -x + 2 Step 1: Substitute -x + 2 for y into 2x + 3y = 10 2x + 3(-x+2) = 10 2x + -3x + 6 = 10 Distribute the 3 -x + 6 = 10 Combine like terms -x + 6 - 6 = 10 -6 Subtract 6 from both sides -x = 4 -x/-1 = 4/-1 Divide by -1 to make x positive x = -4 Step 2: Now we know that x = -4, so we will substitute -4 for x into the equation y = -x + 2 in order to find y. y = -x + 2 y = -(-4) + 2 y = 4 + 2 y = 6 x = -4 & y = 6 The solution is the point (-4, 6) Step 3: Check by substituting: 2x + 3y = 10 2(-4) +3(6) = 10 -8 + 18 = 10 10 = 10 y = -x + 2 6 = -(-4)+2 6 = 4 +2 6 = 6 I hope this helps you in your studies. For more examples using the substitution method, please visit: https://www.algebra-class.com/substitution-method.html Need More Help With Your Algebra Studies?