6x+2y=-3 and 4x-3y=11

Solve the following pair of linear simultaneous equations.

Answer

Multiply all the terms in the top equation by 4. Then multiply all the terms in the bottom equation by 6.

Elimination: Both equations now have a "24x" in the first term. We then subtract the two equations, to eliminate the first term together with the x.

Similarly, we also subtract the "y" terms on the LHS, and the last term after the equal on the RHS to give us the expression above. Remember that minus and minus makes a plus, so the -18 becomes a +18. This might be where students trip up.

Now it is a simple matter of solving for y

Substitute the value of y into the first equation to find the value of x.

It then simplifies to this.

In this step, the "-6" goes on the other side and becomes a "+6".

Solve for x.

Finally, this is the value for x. Solved!