Solving Systems Using the Substitution Method

Please help solve this system using the substitution method.

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

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Apr 18, 2010
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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

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