Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
3. Modeling with Linear Functions
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Exercise 33 Page 28

If either of the variable terms would cancel out the corresponding variable term in the other equation, you can use the Elimination Method to solve the system.

(16,-41)

Practice makes perfect
Since the y-variables have opposite coefficients, we will use the Elimination Method. To solve a system of linear equations this way, one of the variable terms needs to be eliminated when one equation is added to or subtracted from the other equation. 3 x+ y=7 & (I) -2 x- y=9 & (II)We can see that the y-terms will eliminate each other if we add (I) to (II).
3x+y=7 -2x-y=9
3x+y=7 -2x-y+( 3x+y)=9+ 7
3x+y=7 x=16
Now we can solve for y by substituting the value of x into either equation and simplifying.
3x+y=7 x=16
3( 16)+y=7 x=16
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(I):Solve for y
48+y=7 x=16
y=-41 x=16
The solution, or intersection point, of the system of equations is (16,-41).