Topic/Skill Definition/Tips
Topic: Simultaneous Equations Example
1. A set of two or more equations, each 2 x+ y =7
Simultaneous involving two or more variables (letters). 3 x− y=8
Equations
The solutions to simultaneous equations x=3
satisfy both/all of the equations. y=1
2. Variable A symbol, usually a letter, which In the equation x +2=5, x is the
represents a number which is usually variable.
unknown.
3. Coefficient A number used to multiply a variable. 6z
It is the number that comes before/in front 6 is the coefficient
of a letter. z is the variable
4. Solving 1. Balance the coefficients of one of the 5 x+ 2 y =9
Simultaneous variables. 10 x+ 3 y =16
Equations (by 2. Eliminate this variable by adding or Multiply the first equation by 2.
Elimination) subtracting the equations (Same Sign
Subtract, Different Sign Add) 10 x+ 4 y =18
3. Solve the linear equation you get using 10 x+ 3 y =16
the other variable. Same Sign Subtract (+10x on both)
4. Substitute the value you found back into y=2
one of the previous equations.
5. Solve the equation you get. Substitute y=2 in to equation.
6. Check that the two values you get satisfy
both of the original equations. 5 x+ 2× 2=9
5 x+ 4=9
5 x=5
x=1
Solution: x=1 , y=2
5. Solving 1. Rearrange one of the equations into the y−2 x=3
Simultaneous form y=.. . or x=.. . 3 x+ 4 y =1
Equations (by 2. Substitute the right-hand side of the
Substitution) rearranged equation into the other equation. Rearrange: y−2 x=3 → y=2 x+3
3. Expand and solve this equation.
4. Substitute the value into the y=.. . or Substitute: 3 x+ 4 ( 2 x+ 3 )=1
x=.. . equation.
5. Check that the two values you get Solve: 3 x+ 8 x+12=1
satisfy both of the original equations. 11 x=−11
x=−1
Substitute: y=2×−1+3
y=1
Solution: x=−1 , y=1
Mr A. Coleman Glyn School
Topic: Simultaneous Equations Example
1. A set of two or more equations, each 2 x+ y =7
Simultaneous involving two or more variables (letters). 3 x− y=8
Equations
The solutions to simultaneous equations x=3
satisfy both/all of the equations. y=1
2. Variable A symbol, usually a letter, which In the equation x +2=5, x is the
represents a number which is usually variable.
unknown.
3. Coefficient A number used to multiply a variable. 6z
It is the number that comes before/in front 6 is the coefficient
of a letter. z is the variable
4. Solving 1. Balance the coefficients of one of the 5 x+ 2 y =9
Simultaneous variables. 10 x+ 3 y =16
Equations (by 2. Eliminate this variable by adding or Multiply the first equation by 2.
Elimination) subtracting the equations (Same Sign
Subtract, Different Sign Add) 10 x+ 4 y =18
3. Solve the linear equation you get using 10 x+ 3 y =16
the other variable. Same Sign Subtract (+10x on both)
4. Substitute the value you found back into y=2
one of the previous equations.
5. Solve the equation you get. Substitute y=2 in to equation.
6. Check that the two values you get satisfy
both of the original equations. 5 x+ 2× 2=9
5 x+ 4=9
5 x=5
x=1
Solution: x=1 , y=2
5. Solving 1. Rearrange one of the equations into the y−2 x=3
Simultaneous form y=.. . or x=.. . 3 x+ 4 y =1
Equations (by 2. Substitute the right-hand side of the
Substitution) rearranged equation into the other equation. Rearrange: y−2 x=3 → y=2 x+3
3. Expand and solve this equation.
4. Substitute the value into the y=.. . or Substitute: 3 x+ 4 ( 2 x+ 3 )=1
x=.. . equation.
5. Check that the two values you get Solve: 3 x+ 8 x+12=1
satisfy both of the original equations. 11 x=−11
x=−1
Substitute: y=2×−1+3
y=1
Solution: x=−1 , y=1
Mr A. Coleman Glyn School
