Question

solve the following linear equation:
2x - 3y = 3
2x/3 + 4y =6
​

Answer 1

What is the solution to the simultaneous equations 2x+3y=3 and 3x+4y=6?

One method is substitution.

I solve

2x+3y=3

for x because it has the smaller coefficient. Solving for y is acceptable, too.

2x=3−3y

means that

x=3−3y2.

Replace x by this expression in the equation

3x+4y=6

and get

3(3−3y2)+4y=6.

Multiply through by 2 to clear the equation of the fraction:

2(3)(3−3y2)+2(4y)=2(6)

which means that

3(3−3y)+8y=12.

Remove parentheses:

9−9y+8y=12.

Collect terms and get

9−y=12.

Get y by itself:

9−12=y,

that is,

y=−3.

Now go back to the formula obtained for x and replace y by −3:

x=3−3(−3)2=3+92=122,

that is,

x=6.

These answers should be checked in the given equations to make sure that there are no mistakes

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