Simultaneous Equations Practice Questions

Solve the simultaneous equations

$3x + 2y = 16$

$5x - 2y = 16$

Solve the simultaneous equations

$4x + 3y = 6$

$3x - 5y = 19$

Use substitution to solve the simultaneous equations

$y = 2x + 1$

$5x - 2y = 8$

Work out the cost of one box of apples and the cost of one box of pears.

Show that the $x$-coordinates of the points of intersection of the curve and the line satisfy

$x^2 - x - 6 = 0$

Hence solve the simultaneous equations

$y = x^2 + 2x - 5$

$y = 3x + 1$

Use the graph to find estimates for the solutions of $x^2 - 2x - 1 = 0$

By drawing a suitable straight line on the grid, find estimates for the solutions of the simultaneous equations

$y = x^2 - 2x - 1$

$y = x + 1$

Show algebraically that the curve and the straight line meet at exactly one point, and find the coordinates of this point.

What does your answer to part (a) tell you about the straight line $y = x + 3$ and the curve?

Solve algebraically the simultaneous equations

$x^2 + y^2 = 16$

$2y - x = 8$

Work out the total amount of money that Rosie and Sam have.