Solve the following simultaneous equations: 3x+4y=6, 5x+6y=11.

Simultaneous equations can be solved using three methods: elimination, substitution or graphically. The simplest method to solve this example is by elimination. We need to eliminate either x or y by multiplying the equations such that either x or y have the same coefficient. 3x+4y=6 [1]5x+6y=11 [2]In algebra we can multiply and divide an equation by any amount as long as we always do the same thing to both sides. This allows us to find the equivalent coefficient and eliminate x or y.[1]x3: 9x+12y=18 [3][2]x2: 10x+12y=22 [4][4]-[3]: x=4We can substitute x=4 into either equation to find the value of y.3x+4y=63(4)+4y=6 [substituting in x=4]12+4y=6 [multiplying out 3x4]4y=-6 [collecting like terms]y=-6/4 [dividing both sides by 4]y=-3/2 [simplifying]We should now substitute our answers for x and y into the original equations to prove our answers are correct.3x+4y=63(4)+4(-3/2)= 12+-12/2=12-6=6 [correct]5x+6y=115(4)+6(-3/2)=20+18/2=20-9=11 [correct]