Solving By Substitution

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Presentation transcript:

Solving By Substitution

Linear systems can be solved algebraically. One way is to use substitution. This is easiest when one or both equations is given in terms of either x or y. This means that the x or y is alone on one side of the equal sign.

Examples Both equations given in terms of y y = 3x + 2 y = -4x - 7 One in terms of y, one in terms of x y = x + 5 x = 3y - 2 One equation in terms of y y = 2x 3y = x - 1 One equation in terms of x x = 3y -2x = y - 3

Solving With Substitution Solve the linear system: y = 2x + 1 y = 3x - 2

Substitute the value of y in equation 1 into equation 2. Step #1 Substitute the value of y in equation 1 into equation 2. y = 3x – 2  equation 2 y = 2x + 1 equation 1

Substitute the value of y in equation 1 into equation 2. Step #1 Substitute the value of y in equation 1 into equation 2. 2x + 1 = 3x – 2

Step #2 Solve for x: 2x + 1 = 3x - 2 Subtract 2x from both sides. 2x – 2x + 1 = 3x – 2x – 2 1 = x – 2 Add 2 to both sides .. 1 + 2 = x – 2 + 2 3 = x

Substitute the value of x we just found into either equation 1 or 2 Step #3 Substitute the value of x we just found into either equation 1 or 2 y = 2x + 1 y = 2(3) + 1 y = 6 + 1 y = 7

Final Answer Write the final answer as a coordinate point. So, we found our answer to be x = 3 and y = 7. So our solution is (3, 7)

Remember The solution to a linear system is the point of intersection of two equations. That is where the two lines cross and share the same value for x and y.