9.6 Simultaneous Equations

Solve $y = 2x + 1$ and $y = 7$ for $x$ and $y$.

Solve $x + y = 10$ and $x - y = 4$.

Solve $y = 2x$ and $y = 3x - 4$.

Solve $y = 2x + 1$ and $y = 4x + -3$.

Use substitution: $y = 3x$ and $x + y = 12$.

Solve $2x + y = 10$ and $y = x + 1$.

Graphically: which point is on both lines $y = x + 2$ and $y = -x + 4$?

Solve $x = 5$ and $y = 2x - 3$.

Solve $x + 2y = 8$ and $x - 2y = 0$.

Two equations are $y = x + 3$ and $y = 2x + 1$. Find the intersection.

Solve $3x + 2y = 12$ and $x - y = 1$ by elimination.

Solve $y = 4x - 7$ and $2x + y = 5$.

Solve $2x + y = 7$ and $3x - 2y = 21$ by elimination.

Decide whether the system has unique, no, or infinite solutions: $x + y = 3$ and $2x + 2y = 6$.

Solve $y = -x + 6$ and $y = 2x - 3$.

Solve $2(x - 1) + y = 5$ and $3x + 2y = 14$.

Solve $\dfrac{x}{2} + y = 7$ and $x + 2y = 14$.

Find the intersection of $3x + 4y = 12$ and $x = 0$.

Solve $y = 2x + 3$ and $y = -x + 6$ graphically (i.e. find intersection).

Two pens and three pencils cost £1.30. Five pens and one pencil cost £1.90. Find each price.

Use equating $y = y$ method to solve $y = 2x + 1$ and $y = -x + 7$.

A coach hires a 32-seater bus and a 16-seater bus to take 224 students. Total cost £1900 (32-seater £250, 16-seater £150). Find how many of each.

Concert ticket pricing: Friday 50 adult + 20 child = £790; Saturday 80 adult + 40 child = £1320. Find adult and child prices.

A father is 4× his son's age. In 4 years, he will be 3× his son's age. Find their ages.

Solve $\dfrac{x + y}{3} = 5$ and $\dfrac{x - y}{2} = 1$.

Solve $2x + y = 10$ and $x^2 + y = 14$.

A 2-burger meal costs £8.50; a 1-burger + 1-fries meal costs £6.20. Find the prices of a burger and fries.

Three friends share an amount. Alice has £$x$, Bob has £$y$, Charles £$z$. $x + y = 50$, $y + z = 60$, $x + z = 70$. Find each share.

Find the value of $k$ for which $y = 3x + k$ passes through the intersection of $y = 2x + 1$ and $y = x + 4$.

Find the line through the intersection of $y = 2x + 1$ and $y = -x + 7$ that is parallel to $y = 4x - 5$.

Solve $\dfrac{2x + 3y}{5} = 4$ and $3x - y = 7$.

Solve $2x + 3y = 19$ and $4x - y = 17$ using (a) substitution, (b) elimination.

Solve $\dfrac{x + 1}{2} - \dfrac{y - 2}{3} = 1$ and $x + y = 5$.

Two mobile phone tariffs: A: £15 + 10p/min; B: £25 + 5p/min. Find the minutes for equal cost, then which is cheaper for 300 min.

Find the values of $a$ and $b$ such that the system $ax + 2y = 5, 3x + by = 7$ has the solution $(1, 2)$.

A two-digit number has the digit sum 11 and is 27 greater than the number with reversed digits. Find the original number.

Solve $3x - y = 7$ and $x^2 + y^2 = 25$.

A 2-variable system has solution $(2, 3)$. Find the system if both lines pass through this point and one has slope 2 and the other slope $-1$.

A boat travels 36 km downstream in 2 hours and back upstream in 3 hours. Find the speed of the boat in still water and the speed of the current.

Two mixtures: 60% milk and 40% water in mixture A; 20% milk and 80% water in B. How many litres of each to make 10 L of 50% milk-50% water?