1. Solve Linear Systems by Multiplying First Section 7.4 P. 451
2. Steps1. Arrange the equations with like terms in columns.2. Multiply one or both of the the equations by a number to obtain coefficients that are opposites for one of the variables.3. Add /Subt the equations and one term/variable will be eliminated. Solve for the other.4. Substitute the value in Step 3 into either of the original equations. Solve for other variable.5. Check solution in each of the original equations.
3. 6x + 5y = 192x + 3y = 5 Multiply by: ?
4. • Sometimes you need to use a “multiple” of one equation to get terms eliminated. This means multiplying each term by the same number. (Equivalent equations)• Solve 3x = -6y + 12 -x + 3y = 6
5. EXAMPLE 2 Multiply both equations, then subtract Solve the linear system: 4x + 5y = 35 Equation 1 2y = 3x – 9 Equation 2 SOLUTION STEP 1 Arrange: the equations so that like terms are in columns. 4x + 5y = 35 Write Equation 1. –3x + 2y = –9 Rewrite Equation 2.
6. EXAMPLE 2 Multiply both equations, then subtract STEP 2 Multiply: Equation 1 by 2 and Equation 2 by 5 so that the coefficient of y in each equation is the least common multiple of 5 and 2, or 10. 4x + 5y = 35 8x + 10y = 70 –3x + 2y = –9 –15x +10y = –45 STEP 3 Subtract: the equations. 23x = 115 STEP 4 Solve: for x. x=5
7. EXAMPLE 2 Multiply both equations, then subtract STEP 5Substitute: 5 for x in either of the original equationsand solve for y. 4x + 5y = 35 Write Equation 1. 4(5) + 5y = 35 Substitute 5 for x. y=3 Solve for y. ANSWER The solution is (5, 3).
8. • Solve: 2x = 4y + 8 3y = 5x - 13
9. Do P. 454 3-12Show original equation and then newequation (s) through multiplication.Show solution in ordered pair (x, y)
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