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1. [x+y= 10 5x + 4y = 47 %3D %3D

1. [x+y= 10 5x + 4y = 47 %3D %3D

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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3.) S2x +3y -6 12x-16=-8y Example: Solve the following system of equations by substitution. > 2x + 3y = -6 4. 1. -x+y = 5 2x - 5y 1 3. m = b 3D -6 Solution: -5 -4 -3 -2 3. >12x - 16=-8y • First, we will solve the first equation for y. -2 -3 -x+y=-5 -4 b= -5 y= x-5 -6 • Now, we can substitute the expression equation. Then, simplify. 5 for y in the second The graphical method is a good way to find solutions. However, it is not always convenient because some coordinates may involve large numbers or fractions that are difficult to plot. There is another way, the substitution method. 2x 5 1 2x - 5(-5)= 1 2х - 5х + 25-1 -3x =-24 • Now, we substitute x Then, simplify. into the first equation and solve for y. "SOLVING LINEAR SYSTEMS BY SUBSTITUTION" Steps on how to solve a system of two equations in two variables using the substitution method ()+y=-5 y=-5+ 8 y 3 1. Solve one of the two equations for one of the variables in terms of the other. • Therefore, our solution is (8,3). 2. Substitute the expression for this variable into the second equation, then solve for the remaining variable. 3. Substitute that solution into either of the original equations to find the value of the first variable. If possible, write the solution as an ordered pair. 4. Check the solution on both equations. Check the solution by substituting (8,3) into both equations. 2x- 5y 1 2(8)-5(3) 1 16 15 1 -x+y=-5 -(8) + (3) = -5 True -5=-5 1 1 True Cpyht 20o 0 e Cothok Cdcetionc Nghes ered et g MATHENSATICSS 1.
Transcribed Image Text:3.) S2x +3y -6 12x-16=-8y Example: Solve the following system of equations by substitution. > 2x + 3y = -6 4. 1. -x+y = 5 2x - 5y 1 3. m = b 3D -6 Solution: -5 -4 -3 -2 3. >12x - 16=-8y • First, we will solve the first equation for y. -2 -3 -x+y=-5 -4 b= -5 y= x-5 -6 • Now, we can substitute the expression equation. Then, simplify. 5 for y in the second The graphical method is a good way to find solutions. However, it is not always convenient because some coordinates may involve large numbers or fractions that are difficult to plot. There is another way, the substitution method. 2x 5 1 2x - 5(-5)= 1 2х - 5х + 25-1 -3x =-24 • Now, we substitute x Then, simplify. into the first equation and solve for y. "SOLVING LINEAR SYSTEMS BY SUBSTITUTION" Steps on how to solve a system of two equations in two variables using the substitution method ()+y=-5 y=-5+ 8 y 3 1. Solve one of the two equations for one of the variables in terms of the other. • Therefore, our solution is (8,3). 2. Substitute the expression for this variable into the second equation, then solve for the remaining variable. 3. Substitute that solution into either of the original equations to find the value of the first variable. If possible, write the solution as an ordered pair. 4. Check the solution on both equations. Check the solution by substituting (8,3) into both equations. 2x- 5y 1 2(8)-5(3) 1 16 15 1 -x+y=-5 -(8) + (3) = -5 True -5=-5 1 1 True Cpyht 20o 0 e Cothok Cdcetionc Nghes ered et g MATHENSATICSS 1.
Substitution,you may open your book and refer to pages 181-184 ***To learn more about Solving Linear Svstens by Let's check your understanding by answering the following "SOLVING LINEAR SYSTEMS BY ELIMINATION" Steps on how to solve a system of equations using the Elimination Method. Direction: Solve the following systems of linear equations in two variables by substitution method. 1. Write both equations with x-- and y-variables on the left side of the equal sign and constants on the right. { 1. [x+y 10 (5x + 4y = 47 2. Write one equation above the other, lining up corresponding variables. If one of the variables in the top equation has the opposite coefficient of the same variable in the bottom equation, add the equations together, eliminating one variable. If not, use multiplication by a nonzero number so that one of the variables in the top equation has the opposite coefficient of the same variable in the bottom equation, then add the equations to eliminate the variable. 3. Solve the resulting equation for the remaining variable. 4. Substitute that value into one of the original equations and solve for the second variable. [x=y+3 4 = 3x - 2y 5. Check the solution by substituting the values into the other equation. Example: Solve the given system of equations by Elimination. x + 2y = -1 -x+y = 3 1.) Solution: • Both equations are already set equal to a constant. Notice that the coefficient of x in the second equation, -1, is the opposite of the coefficient of x in the first equation, 1. We can add the two equations to eliminate x without needing to multiply by a constant. Another algebraic method can be used to avoid the inconveniençe of working with fractions. This method is called -> 2.
Transcribed Image Text:Substitution,you may open your book and refer to pages 181-184 ***To learn more about Solving Linear Svstens by Let's check your understanding by answering the following "SOLVING LINEAR SYSTEMS BY ELIMINATION" Steps on how to solve a system of equations using the Elimination Method. Direction: Solve the following systems of linear equations in two variables by substitution method. 1. Write both equations with x-- and y-variables on the left side of the equal sign and constants on the right. { 1. [x+y 10 (5x + 4y = 47 2. Write one equation above the other, lining up corresponding variables. If one of the variables in the top equation has the opposite coefficient of the same variable in the bottom equation, add the equations together, eliminating one variable. If not, use multiplication by a nonzero number so that one of the variables in the top equation has the opposite coefficient of the same variable in the bottom equation, then add the equations to eliminate the variable. 3. Solve the resulting equation for the remaining variable. 4. Substitute that value into one of the original equations and solve for the second variable. [x=y+3 4 = 3x - 2y 5. Check the solution by substituting the values into the other equation. Example: Solve the given system of equations by Elimination. x + 2y = -1 -x+y = 3 1.) Solution: • Both equations are already set equal to a constant. Notice that the coefficient of x in the second equation, -1, is the opposite of the coefficient of x in the first equation, 1. We can add the two equations to eliminate x without needing to multiply by a constant. Another algebraic method can be used to avoid the inconveniençe of working with fractions. This method is called -> 2.
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