Linear Equations Practice Problems Worksheet

📆 Updated: 1 Jan 1970
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🔖 Category: Line

This linear equations practice problems worksheet is designed to provide valuable practice for students who want to enhance their skills in solving equations. With a focus on entities and subjects, this worksheet serves as an excellent tool for middle and high school students who are looking to solidify their understanding of linear equations and build their problem-solving capabilities.



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Solve 2x + 5 = 15 for x.

To solve the equation 2x + 5 = 15 for x, we first subtract 5 from both sides to isolate 2x. This gives us 2x = 10. Then, we divide by 2 on both sides to find x. Therefore, x = 5.

Find the equation of a line passing through the points (2, 4) and (5, -2).

To find the equation of a line passing through two points (x?, y?) and (x?, y?), first calculate the slope using the formula m = (y? - y?) / (x? - x?). Substituting the given points yields m = (-2 - 4) / (5 - 2) = -6 / 3 = -2. Then, use the point-slope form of the equation of a line: y - y? = m(x - x?). With the slope and one point, plug in m = -2, x? = 2, and y? = 4 to get the equation y - 4 = -2(x - 2), which simplifies to y = -2x + 8. Hence, the equation of the line passing through the points (2, 4) and (5, -2) is y = -2x + 8.

Simplify 3(2x - 4) - 2(x + 3).

To simplify the expression 3(2x - 4) - 2(x + 3), first distribute the coefficients: 6x - 12 - 2x - 6. Next, combine like terms: 6x - 2x - 12 - 6 = 4x - 18. Therefore, the simplified expression is 4x - 18.

Solve the system of equations: 2x + y = 7 and 3x - 2y = 4.

To solve the system of equations 2x + y = 7 and 3x - 2y = 4, we can start by solving the first equation for y to get y = 7 - 2x. Then, we can substitute this expression for y into the second equation: 3x - 2(7 - 2x) = 4. Simplifying this equation, we get x = 2. Substituting x = 2 into the first equation gives us y = 3. Therefore, the solution to the system of equations is x = 2 and y = 3.

Determine the slope-intercept form of the equation with a slope of 2 and y-intercept of -3.

The slope-intercept form of the equation is y = 2x - 3.

Solve 5x + 3 = 2x - 4 for x.

To solve the equation 5x + 3 = 2x - 4 for x, first simplify by moving all terms involving x to one side of the equation. Subtracting 2x from both sides gives 3x + 3 = -4. Next, subtract 3 from both sides to isolate x, resulting in 3x = -7. Finally, divide both sides by 3 to solve for x, which gives x = -7/3 or x = -2.33 as a decimal.

Find the value of y when x = 3 in the equation 2x - 4y = 10.

To find the value of y when x = 3 in the equation 2x - 4y = 10, substitute x = 3 into the equation. This gives us 2(3) - 4y = 10, which simplifies to 6 - 4y = 10. Rearranging the equation, we get -4y = 4, and dividing by -4 gives us y = -1. Therefore, when x = 3, y = -1 in the equation 2x - 4y = 10.

Write the equation of a line that is perpendicular to y = 2x + 3 and passes through the point (4, -1).

The given line has a slope of 2. Therefore, a line perpendicular to it would have a slope that is the negative reciprocal of 2, which is -1/2. Using the point-slope form of a linear equation, we have: y - (-1) = -1/2(x - 4). Simplifying this equation gives us y + 1 = -1/2x + 2. Rearranging terms gives the equation of the line as y = -1/2x + 1.

Solve 3(4x - 1) + 2(x + 5) = 13 for x.

To solve the equation 3(4x - 1) + 2(x + 5) = 13 for x, you would first distribute the coefficients to their respective terms: 12x - 3 + 2x + 10 = 13. Combine like terms to simplify the equation: 14x + 7 = 13. Then isolate x by subtracting 7 from both sides to get 14x = 6, and finally divide by 14 to solve for x. Therefore, x = 6/14 which simplifies to x = 3/7.

Determine whether the lines represented by the equations -4x + 2y = 8 and 8x - 4y = -16 are parallel, perpendicular, or neither.

The lines represented by the given equations -4x + 2y = 8 and 8x - 4y = -16 are parallel because they have the same slope. The first equation can be rewritten as y = 2x + 4, and the second equation as y = 2x + 4, confirming that both equations have a slope of 2, indicating that the lines are parallel.

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