Algebra Substitution Worksheets

Algebra substitution worksheets provide a valuable resource for students seeking to solidify their understanding of the essential concept of substitution in algebraic equations. These worksheets offer a range of practice problems and exercises that focus on substituting values for variables, helping students build confidence and mastery in working with algebraic expressions. Whether you are a student looking to strengthen your skills or a teacher searching for additional resources, algebra substitution worksheets can be a beneficial tool for enhancing learning in this area.

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Solve the equation 3x - 2 = 10 using substitution.

To solve the equation 3x - 2 = 10 using substitution, first isolate the variable x by adding 2 to both sides of the equation: 3x = 12. Then, divide both sides by 3 to find the value of x: x = 4. Therefore, the solution to the equation 3x - 2 = 10 is x = 4.

Find the value of y in the equation y + 4 = 2x + 5 when x = 3.

When x = 3, we can substitute the value into the equation y + 4 = 2(3) + 5. This simplifies to y + 4 = 6 + 5, which further simplifies to y + 4 = 11. By subtracting 4 from both sides of the equation, we find that y = 7. Therefore, the value of y when x = 3 is y = 7.

Determine the solution to the system of equations 2x - y = 5 and x + y = 7 using substitution.

By solving the second equation for y, we get y = 7 - x. Substituting this into the first equation, we have 2x - (7 - x) = 5. Simplifying, we get 2x - 7 + x = 5, which leads to 3x - 7 = 5. Adding 7 to both sides gives 3x = 12, and dividing by 3 yields x = 4. Substituting x = 4 back into y = 7 - x, we get y = 7 - 4, which gives y = 3. Therefore, the solution to the system of equations 2x - y = 5 and x + y = 7 is x = 4 and y = 3.

Calculate the value of z in the equation 4z - 3 = 2(z + 1) - 5.

To solve for z in the equation 4z - 3 = 2(z + 1) - 5, first distribute the 2 on the right side to get 4z - 3 = 2z + 2 - 5. Combining like terms gives 4z - 3 = 2z - 3. Then, subtract 2z from both sides to isolate z, which results in 2z - 3 = -3. Finally, add 3 to both sides to find that 2z = 0, and dividing by 2 gives z = 0. Thus, the value of z in this equation is 0.

Solve the equation 2(3x - 4) = 8x - 6 using substitution.

To solve the equation 2(3x - 4) = 8x - 6 using substitution, we first simplify the left side by distributing the 2, resulting in 6x - 8 = 8x - 6. Next, we isolate variables on one side by subtracting 6x from both sides, yielding -8 = 2x - 6. Then, we add 6 to both sides to get -2 = 2x. Finally, we divide by 2 on both sides, giving us x = -1 as the solution to the equation.

Find the solution to the system of equations y = 2x - 1 and 3x + 2y = 10 using substitution.

Substitute y = 2x - 1 into the second equation: 3x + 2(2x - 1) = 10. Simplifying the equation gives 3x + 4x - 2 = 10. Combining like terms results in 7x - 2 = 10. Adding 2 to both sides leads to 7x = 12. Dividing by 7 gives x = 12/7. Substitute x back into the first equation y = 2(12/7) - 1 to find y. So, y = 24/7 - 7/7 = 17/7. Therefore, the solution to the system of equations is x = 12/7 and y = 17/7.

Determine the value of a in the equation 2(a - 3) + 4 = 5 - (a + 1).

To determine the value of a in the equation 2(a - 3) + 4 = 5 - (a + 1), we can start by simplifying both sides of the equation. First, distribute the 2 on the left side to get 2a - 6 + 4 = 5 - a - 1. This simplifies to 2a - 2 = 4 - a. Next, add 'a' to both sides to get 3a - 2 = 4. Then, add 2 to both sides to isolate 'a' and get 3a = 6. Finally, divide by 3 to find that a = 2.

Solve the equation 5(2x - 3) = 3(4 - x) using substitution.

To solve the equation 5(2x - 3) = 3(4 - x) using substitution, we first expand both sides to simplify the equation. On the left side, we get 10x - 15, and on the right side, we get 12 - 3x. Now we have the equation 10x - 15 = 12 - 3x. Next, we can add 3x to both sides to get 13x - 15 = 12. Adding 15 to both sides gives us 13x = 27. Finally, dividing by 13, we find that x = 27/13 or 2.0769 (rounded to four decimal places).

Find the solution to the system of equations 3x + 2y = 9 and 5x - y = 4 using substitution.

To solve the system of equations using substitution, isolate y in the second equation: y = 5x - 4. Substitute this expression for y into the first equation: 3x + 2(5x - 4) = 9. Simplify to get 13x - 8 = 9, or 13x = 17. Solving for x gives x = 17/13. Substitute x back into y = 5x - 4 to find y: y = 5(17/13) - 4, which reduces to y = 25/13. Therefore, the solution to the system of equations is x = 17/13 and y = 25/13.

Determine the value of k in the equation 2(k + 3) = 5 - (k - 2).

To find the value of k in the equation 2(k + 3) = 5 - (k - 2), we need to simplify it first. Distributing on the left side gives 2k + 6, and combining like terms on the right side gives 5 - k + 2, which simplifies to 7 - k. Therefore, we have 2k + 6 = 7 - k. Solving for k by moving terms around, we get 3k = 1, and dividing by 3 gives k = 1/3. Hence, the value of k in the equation is 1/3.