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Solving Using Substitution where the lines intersect. So the solution could bewhich of the following? A solution to a system of equations is A single point (one ordered pair) No solution (parallel lines; they don't intersect) Infinite # of Solutions (same line) all of the above 1. Solve for the other variable. 2. Substitute the # or expression in forthe isolated variable. 4. Isolate one of the variables. 3. Take the answer you got, and plug it into one of the equations to find the othervariable. 5. Write the ordered pair. Put the steps in order for solving a system using the method of substitution. 4, 2, 1, 3, 5 1, 4, 2, 3, 5 2, 1, 4, 3, 5 4, 3, 2, 1, 5 { Solve by Substitution. Fill in the blanks. 3x - 1 = 2x - 1 = 5 y = 3x - 1 y = x + 5 2x = 6 x = 3 Answer ( y = 3 • y = y = 8 9 - 1 , - 1 ) Solve by substitution. Fill in the blanks. 2 + 3y = 21 { y = ( 2x + 3y = 21 x = 9 ) So, the solution is ( , ) Solve by substitution. Fill in the blanks. { y = -2x + 1 y = 4x - 5 = 4x - 5 ( , ) Step 1: Solve for x in the 2nd equation. Step 2: Substitute the expression into the otherequation. Solve by Substitution. Fill in the blanks. Step 3: Solve for y! x = -2y - 1 { y = 3x - 2y = 13 x + 2y = -1 3 ( ) - 2y = 13 Step 5: Write the ordered pair. Step 4: Substitute the y value into either equation. The solution is: ( , ) Solve the system. { y = 4x + 2 y = 10 Answer: ( , ) Is (-4, -1) a solution of { 3x - 2y = -10 5x - 11y = -9 ? yes no Solve the system. { 2x - y = 1 y = 10 Answer: ( , ) Solve the system. { 4x -2y = 10 x = 4 Answer: ( , ) Solve the system. { y = -5x + 1 5x + 2y = 7 Answer: ( , ) What would be the first step when solving this system using substitution? Substitute (7x - 5y) for x in the first equation Substitute (x + 3) for y in the second equation Substitute (y + 3) for y in the second equation Substitute (y + 3) for x in the second equation { x = y + 3 7x - 5y = 19 There is no next step. You are done. Plug -3 in for x into either original equation to find y What would the next step to find the solution? { -2x - y = -2 y = x - 1 Plug 1 in for y into either equation to find x Plug 1 in for x into either original equation to find y -2x - (x - 1) = -2 -3x + 1 = -2 -3x = -3 x = 1 (This means they are parallel lines!) When our variables disappear and we are left with a false statement, the answer is "no solution". (This means they are completely overlapping!) When our variables disappear and we are left with a true statement, the answer is "infinitely many". Infinitely many 4x - 2y = 4 y = 2x - 2 4x - 2(2x - 2) = 4 4x - 4x + 4 = 4 4 = 4 Solve the system. { 4x -2y = 10 y =2x +5 Infinitely many No solution Solve the system. { 3x+ y = 6 y = -3x + 6 Infinitely many No solution |