Practice: systems of equations
Practice: systems of equations
Which of the pairs is the solution of the system: , , ?
Explain by substituting.
Here are the lines of the system
Mark the point where they meet on the graph.
Write the solution of the system, and check it by substituting into both equations.
Without solving: how many solutions does each system have – one, none or infinitely many?
Explain.
Solve by substitution.
Solve by comparison.
Solve by adding or subtracting the equations.
In parts 3 and 4 first multiply an equation by a number – or both of them.
The sum of two numbers is 50, and their difference is 14.
Find the two numbers.
Write a system of equations and solve it.
2 notebooks and 3 pens cost 27 ₪.
4 notebooks and 1 pen cost 29 ₪.
How much is a notebook, and how much a pen?
Write a system of equations and solve it.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Grandma’s yard has hens and rabbits.
Together they have 20 heads and 56 legs.
How many hens and how many rabbits are in the yard?
Write a system of equations and solve it.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
In a basketball game a team scored 23 baskets: 2-point baskets and 3-point baskets.
The team scored 52 points in the game.
How many baskets of each kind did the team score?
Write a system of equations and solve it.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
There are two gyms in town:
Gym A charges a 100 ₪ sign-up fee plus 30 ₪ a month.
Gym B charges 50 ₪ a month, with no sign-up fee.
On the graph, is the number of months and the total price in shekels; gym B is the dashed line.
Mark the point where the lines meet on the graph.
Write an equation and solve it: after how many months do the two gyms cost the same?
Yoav wants to train for a whole year. Which gym should he join?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power