  # intersection of x + 3y and y = -1, linear equations

1. The lines x + 3y and y = -1 intersect at x =

2. The vertical intercept of the line 5 - 4x is y =

3. The solution of 5x - 3 = 2x - 9
is x =

4. Simplified the following expression:
a) p + 4q + 5p + q^2
b) p - 4q + 5p + q^2
C) q - 4q + 5p + q^2
D) q + 4q + 5p + q^2

6.Find the horizontal intercept/s of x^2 - 2x - 3

7.Find the vertical intercep of y = x^2 + 16

8.Find the solution of 10q = 2q + 100
is q =

9.If PV = 100,r=0.03 and n = 5 evaluate to 2 decimal places
FV = PV (1+r)^n

10. If q = 1000 evaluate
p = 100 - 0.1q

11. Evaluate 10 + (-3.3)

12. Evaluate (-3) X (-2.5)

13. Cakculate 215% of 150

14. Solve for t
2e^t = 26.927 Give answer to one decimal place.

15. Express 375/300 as percentage.

### Comments for intersection of x + 3y and y = -1, linear equations

 May 29, 2012 Algebra Problems by: Staff Part I Question: 1. The lines x + 3y and y = -1 intersect at x = 2. The vertical intercept of the line 5 - 4x is y = 3. The solution of 5x - 3 = 2x - 9 is x = 4. Simplified the following expression: a) p + 4q + 5p + q^2 b) p - 4q + 5p + q^2 C) q - 4q + 5p + q^2 D) q + 4q + 5p + q^2 6.Find the horizontal intercept/s of x^2 - 2x - 3 7.Find the vertical intercept of y = x^2 + 16 8.Find the solution of 10q = 2q + 100 is q = 9.If PV = 100,r=0.03 and n = 5 evaluate to 2 decimal places FV = PV (1+r)^n 10. If q = 1000 evaluate p = 100 - 0.1q 11. Evaluate 10 + (-3.3) 12. Evaluate (-3) X (-2.5) 13. Calculate 215% of 150 14. Solve for t 2e^t = 26.927 Give answer to one decimal place. 15. Express 375/300 as percentage. Answer: 1. The lines x + 3y and y = -1 intersect at x = There is information missing from the problem statement. y = -1 is valid. This is a horizontal line at y = -1 x + 3y is not a line. It is an expression. To be a valid equation there must be an EQUAL SIGN, such as: x + 3y = 0 Assuming the two equations are: x + 3y = 0 y = -1 The answer is: x + 3y = 0 x + 3*(-1) = 0 x - 3 = 0 x - 3 + 3 = 0 + 3 x + 0 = 0 + 3 >>> x = 3 2. The vertical intercept of the line 5 - 4x is y = There is also information missing from this problem statement. 5 - 4x is an expression, not an equation. To be an equation there must be an EQUAL sign, such as: 5 - 4x = y Assuming the equation is: 5 - 4x = y The answer is: 5 - 4x = y y = 5 - 4x y = 5 - 4*0 y = 5 - 0 >>> y = 5 3. The solution of 5x - 3 = 2x - 9 is x = 5x - 3 = 2x - 9 5x - 3 - 2x = 2x - 9 - 2x 5x - 2x - 3 = 2x - 2x - 9 (5x - 2x) - 3 = (2x - 2x) - 9 3x - 3 = 0 - 9 3x - 3 = - 9 3x - 3 + 3 = - 9 + 3 3x + 0 = - 6 3x = - 6 3x / 3 = - 6 / 3 x * (3 / 3) = (- 6 / 3) x * (1) = (- 6 / 3) x = (- 6 / 3) >>> x = -2 ----------------------------------------------------

 May 29, 2012 Algebra Problems by: Staff ---------------------------------------------------- Part II 4. Simplify the following expression: a) p + 4q + 5p + q² p + 4q + 5p + q² = q² + p + 5p + 4q >>> q² + 6p + 4q b) p - 4q + 5p + q² = q² + p + 5p - 4q >>> q² + 6p - 4q C) q - 4q + 5p + q² = q² + 5p + q - 4q >>> q² + 5p - 3q D) q + 4q + 5p + q² = q² + 5p + q + 4q >>> q² + 5p + 5q 6.Find the horizontal intercept/s of x^2 - 2x - 3 There is information missing from the problem statement. x² - 2x - 3 is not an equation, and does not have horizontal intercepts. It is an expression. To be a valid equation there must be an EQUAL SIGN, such as: x² - 2x - 3 = f(x) Assuming the equation is: x² - 2x - 3 = f(x) The answer is the answer can be computed using the quadratic equation: ax² + bx + c = 0 x = [-b ± √(b² - 4ac)]/(2a) Or, you can just factor it: x² - 2x - 3 = 0 (x - 3)(x + 1) = 0 x₁ - 3 = 0 x₁ - 3 + 3 = 0 + 3 x₁ = 3 x₂ + 1 = 0 x₂ + 1 - 1 = 0 - 1 x₂ = - 1 >>> the final answer is: x ∈{-1, 3} 7.Find the vertical intercept of y = x^2 + 16 The vertical intercept will occur when x = 0 y = x² + 16 y = 0² + 16 y = 16 >>> the vertical intercept occurs at the point (0,16) 8.Find the solution of 10q = 2q + 100 is q = 10q = 2q + 100 10q - 2q = 2q + 100 - 2q 10q - 2q = 2q - 2q + 100 8q = 0 + 100 8q = 100 8q / 8 = 100 / 8 q * (8 / 8) = 100 / 8 q * (1) = 100 / 8 q = 100 / 8 >>> q = 12.5 9.If PV = 100,r=0.03 and n = 5 evaluate to 2 decimal places FV = PV (1+r)^n FV = 100 * (1 + .03)⁵ FV = 100 * (1.03)⁵ FV = 100 * 1.1592740743 >>> FV = 115.93 10. If q = 1000 evaluate p = 100 - 0.1q p = 100 - 0.1 * 1000 p = 100 - 100 >>> p = 0 11. Evaluate 10 + (-3.3) 10 + (-3.3) = 10 - 3.3 >>> = 6.7 12. Evaluate (-3) X (-2.5) (-3) * (-2.5) >>> +7.5 13. Calculate 215% of 150 215% of 150 = 215% * 150 = (215 / 100) * 150 = 2.15 * 150 >>> 322.5 14. Solve for t 2e^t = 26.927 Give answer to one decimal place. 2e^t = 26.927 2e^t / 2= 26.927 / 2 e^t = 26.927 / 2 log_base e_(e^t) = log_base e_(13.4635) t = log_base e_(13.4635) t = ln(13.4635) t ≈ 2.5999823201324 >>> t ≈ 2.6 15. Express 375/300 as percentage. (%) / 100 = 375/300 (%) = (375/300)*100 (%) = 125 >>> 125 % Thanks for writing. Staff www.solving-math-problems.com