Sec 2 Mathematics Linear Graphs & Simultaneous Equations topical questions

For the linear function y = 2x − 1:

1. (a)Find y when x = −1, 0, 1 and 2.[2]
2. (b)State the gradient.[1]
3. (c)State the coordinates of the y-intercept.[1]

Points P(−3, −4), Q(5, −2) and R(0, 6) are marked on a grid.

1. (a)Name the quadrant of P.[1]
2. (b)Name the quadrant of Q.[1]
3. (c)Explain why R lies on an axis, and name the axis.[2]

For the line y = 3x − 6:

1. (a)Find y when x = 2.[1]
2. (b)Find x when y = 0.[1]
3. (c)State where the line crosses the y-axis.[1]
4. (d)Does the point (4, 6) lie on the line? Show how you decide.[1]

For the linear function y = −x + 5:

1. (a)Find y when x = 0, 1 and 2.[1]
2. (b)State the gradient.[1]
3. (c)State the coordinates of the y-intercept.[1]

Name the quadrant (or axis) of each point.

1. (a)(4, −1)[1]
2. (b)(−5, 2)[1]
3. (c)(−2, −7)[1]

Find the gradient of the line through each pair of points.

1. (a)(2, 3) and (6, 11)[2]
2. (b)(−1, 4) and (3, 0)[2]

A linear equation is given as 3x + 2y = 12.

1. (a)Rearrange it into the form y = mx + c.[2]
2. (b)State the gradient and the y-intercept.[2]

The lines y = x + 1 and y = −x + 5 are drawn on the same axes.

1. (a)Complete both tables of values for x = 0, 1, 2, 3, 4.[1]
2. (b)For which x-value do the two lines have the same y-value?[2]
3. (c)State the solution of the pair as coordinates.[1]

Solve the pair 3x + 2y = 16 and x − 2y = 0 by elimination.

1. (a)Explain why adding the equations eliminates y.[1]
2. (b)Solve the pair.[2]
3. (c)Check your solution in the equation you did not use.[1]

A linear equation is given as 2x + 3y = 6.

1. (a)Rearrange it into the form y = mx + c.[2]
2. (b)State the gradient.[1]
3. (c)Find the x-intercept.[1]

At a hawker centre, Mr Lim buys 2 plates of carrot cake and 1 drink for $5.10. Mrs Lim buys 1 plate of carrot cake and 2 drinks for $4.50.

1. (a)Write a pair of simultaneous equations, defining your letters.[1]
2. (b)Solve the pair by substitution or elimination.[2]
3. (c)Check your answers in the receipt you did not use.[1]

Solve the pair 2x + y = 11 and y = x + 2 by substitution.

1. (a)Substitute the second equation into the first, keeping the brackets.[2]
2. (b)Solve for x.[1]
3. (c)Find y and state the full solution.[2]

Solve the pair 3x + 2y = 19 and 2x + 3y = 21 by elimination. Neither equation can cancel a letter directly.

1. (a)State which variable you will eliminate and what you multiply each equation by.[1]
2. (b)Write the two transformed equations and the equation that results from eliminating.[2]
3. (c)Solve the pair completely.[2]

At a cinema, 2 adult tickets and 3 child tickets cost $24. One adult and one child ticket together cost $10.

1. (a)Write a pair of simultaneous equations for the two receipts.[2]
2. (b)Solve the pair to find each ticket price.[2]
3. (c)Find the total cost of 4 adult and 5 child tickets.[1]

A line passes through the point (2, 5) with gradient 3.

1. (a)Explain why its equation is y = 3x − 1.[2]
2. (b)State the y-intercept.[1]
3. (c)Show that the point (10, 29) lies on the line.[1]
4. (d)Find where this line meets y = x + 1.[1]