4x-y=3 and 3x-2y=1. Solve these simultaneous equations to find values for x and y.
Equation 1: 4x-y=3 Equation 2: 3x-2y=1
We have to find a common multiple between 4 and 3 so that both equations have the same first value. This means that we can get rid of the x by subtracting the second equation from the first. This will leave us with a simple linear equation with which we can solve to find y and then go on to find x. The lowest common denominator between 4 and 3 is 12.
3(4x-y)=3x3 -> 12x-3y=9 (Eq. 1)
4(3x-2y)=4x1 -> 12x-8y=4 (Eq. 2)
Eq. 1 - Eq.2 = 12x-12x-3y--8y=9-4 -> 5y=5
hence y=1 and now we have to input the y value into the first (or second) equation to find x
4x-1=3 -> 4x=4 -> x=1
So x=1 and y=1
JH
Related Maths GCSE answers
All answers ▸Talil is going to make some concrete mix. He needs to mix cement, sand and gravel (1: 3:5) by weight. Talil wants to make 180 kg of concrete mix. He has 15 kg of cement, 85 kg of sand, 100 kg of gravel. Does he have enough to make the concrete?
Solve the simultaneous equations: 1) 3x+5y=14 and 2) -3y+10=x
Solve the simultaneous equations. 3x + 5y = 1 , 2x - 3y = 7
A circle with diameter 6cm is cut from a square with side length 7cm. What is the remaining area of the square? You may assume pi = 3 for this question.