SYSTMES OF EQUATIONS SUBSTITUTION.

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Solving a system of equations by SUBSTITUTION

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Presentation transcript:

SYSTMES OF EQUATIONS SUBSTITUTION

WARM UP Simplify: 4(2x – 2) = 3 x + 5 Solve for y: 2x – 3y = 9. Draw a line to represent this equation. How many solutions does this system have? y = 3x – 5 and y = 3x + 2 Solve this system using substitution: y = 4x and y = x + 3

Solving a system of equations by substitution Step 1: Solve an equation for one variable. Pick the easier equation. The goal is to get y= ; x= ; a= ; etc. Put the equation solved in Step 1 into the other equation. Step 2: Substitute Step 3: Solve the equation. Get the variable by itself. Substitute the value of the variable into the equation. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Substitute your ordered pair into BOTH equations.

Solve the system using substitution x + y = 5 y = 3 + x Step 1: Solve an equation for one variable. The second equation is already solved for y! Step 2: Substitute x + y = 5 x + (3 + x) = 5 Step 3: Solve the equation. 2x + 3 = 5 2x = 2 x = 1

x + y = 5 y = 3 + x Step 4: Plug back in to find the other variable. x + y = 5 (1) + y = 5 y = 4 Step 5: Check your solution. (1, 4) (1) + (4) = 5 (4) = 3 + (1) The solution is (1, 4). What do you think the answer would be if you graphed the two equations?

Solve these systems using substitution. Show all your work. Check your answer using the calculator.

It is easiest to solve the Solve the system using substitution 3y + x = 7 4x – 2y = 0 It is easiest to solve the first equation for x. 3y + x = 7 -3y -3y x = -3y + 7 Step 1: Solve an equation for one variable. 4x – 2y = 0 4(-3y + 7) – 2y = 0 Step 2: Substitute

3y + x = 7 4x – 2y = 0 (1, 2) 3(2) + (1) = 7 4(1) – 2(2) = 0 Step 3: Solve the equation. -12y + 28 – 2y = 0 -14y + 28 = 0 -14y = -28 y = 2 Step 4: Plug back in to find the other variable. 4x – 2y = 0 4x – 2(2) = 0 4x – 4 = 0 4x = 4 x = 1 (1, 2) 3(2) + (1) = 7 4(1) – 2(2) = 0 Step 5: Check your solution.

Solve these systems using substitution. Show all your work. Check your answer using the calculator. 6x – 5y = 22 y = -8 y = -8 2x + 4y = 0 5x + 5y = 0 3x + 10y = -42