Linear Equations Practice

Solve the equation 2x + 3y = 12 for y.

• y = (12 + 2x) / 3

• y = (12 - 3x) / 2

• y = (12 - 2x) / 3

• y = (12 + 3x) / 2

Answer explanation

To solve for y, isolate y in the equation 2x + 3y = 12. Subtract 2x from both sides to get 3y = 12 - 2x. Then divide by 3 to find y = (12 - 2x) / 3.

Find the value of x if 5x - 2y = 8 and y = 3.

• x = 2.8

• x = 1.9

• x = 4.2

• x = 3.5

Answer explanation

Substitute y = 3 into the equation 5x - 2(3) = 8. Simplify to get 5x - 6 = 8. Add 6 to both sides to get 5x = 14. Divide by 5 to find x = 2.8.

Determine if the point (4, 2) lies on the line 3x - 2y = 8.

• Sometimes

• Maybe

• Yes

• No

Answer explanation

Substitute x = 4 and y = 2 into the equation 3x - 2y = 8. 3(4) - 2(2) = 12 - 4 = 8, which satisfies the equation. Therefore, the point (4, 2) lies on the line 3x - 2y = 8. The correct answer is Yes.

Write the equation of a line passing through the points (1, 3) and (5, 7).

• y = -x + 5

• y = x + 2

• y = 3x + 4

• y = 2x + 1

Answer explanation

To find the equation of the line passing through two points, calculate the slope (m) using (y2-y1)/(x2-x1). Then use the point-slope form y - y1 = m(x - x1) with either point to get y = x + 2.

If 4x + 3y = 20, what is the value of y when x = 2?

• 10

• 8

• 4

• 6

Answer explanation

Substitute x=2 into the equation 4x + 3y = 20 to get 4(2) + 3y = 20. Simplify to 8 + 3y = 20. Then, solve for y to get y = 4. Therefore, the value of y when x=2 is 4.

Simplify the expression 2(3x - 4y) - 5(2x + y).

• -4x - 13y - 2

• -4x - 13y + 2

• -4x - 13y

• -4x + 13y

Solve the system of equations: 2x + y = 7 and x - 3y = -5.

• x = -2, y = 5

• x = 4, y = 3

• x = 6, y = 17/7

• x = 8, y = -1

Answer explanation

To solve the system of equations, we can use the method of substitution or elimination. By solving the equations simultaneously, we find x = 6 and y = 17/7, which matches the correct answer choice.

Find the slope of the line passing through the points (2, 5) and (4, 9).

• 6

• 4

• 3

• 2

Answer explanation

To find the slope, use the formula (y2 - y1) / (x2 - x1) with the points (2, 5) and (4, 9). This gives (9 - 5) / (4 - 2) = 4 / 2 = 2. Therefore, the slope is 2.

If 3x - 2y = 10, what is the value of x when y = 2?

• x = 14/3

• x = 5

• x = 2

• x = 8

Answer explanation

Substitute y = 2 into 3x - 2y = 10 to get 3x - 2(2) = 10. Solve for x to get x = 14/3.

Determine if the lines 4x - 2y = 8 and 2x - y = 4 are parallel, intersecting, or coincident.

• coincident

• intersecting

• perpendicular

• parallel

Answer explanation

The lines are coincident because they represent the same line. By rearranging the second equation, we get 4x - 2y = 8, which is the same as the first equation. Therefore, they coincide.