Solve 2x+y=6, 3x+2y=3 for x and y.
Give each equation a label:(1) 2x+y=6(2) 3x+2y=3Multiply one equation to make the number of x's or y's the same in each equation. 2 X (1) : 2(2x+y=6) 4x+2y=12 (2) 3x+2y=3There are now 2y's in each equation therefore will cancel each other out in next sum.Either add or subtract one equation from other depending of signs of equal letters (in this case y), if signs are the same, (eg. +2y and +2y) then subtract ( eqn (1) - eqn (2) ). If the signs are different (eg. +2y - 2y) then add ( eqn (1) + eqn (2) ). In this case the signs are the same therefore we will subtract. 2 X (1): 4x+2y=12 -(2) - 3x+2y=3, x =9Substitute x=9 into equation (1): 2x+y=6 2(9)+y=6 18+y=6 y=6-18 y=-12Substitute x and y values into equation (2) to check answer is correct:3x+2y=3LHS= 3(9)+2(-12) 27-24 3RHS=3Therefore LHS=RHS, so we know that x=9 and y=-12.
Related Maths GCSE answers
All answers ▸The perimeter of an isosceles triangle is 16cm. The length of the base of the triangle is x+4 and that of the other two sides is x+3. Find the area of the triangle
simplify fully: (x^2+x-6)/(x^2-7x+10)
Find the nth term in the series: 3, 7, 11, 15, 19
A bag contains only 8 beads. The beads are identical in all respects except colour. 3 of the beads are black and the other 5 beads are white. A bead is taken at random from the bag and not replaced. A second bead is then taken at random from the bag. What