Question

2x + 3y = 7
3x + 12y = 9
What is x and y?

Answer 1

You could use a sub

Answer 2

sub?

Answer 3

Substitution

Answer 4

dont know how..

Answer 5

Second equation, you could solve for x

Answer 6

Does it matter what method we use? Eliminate/ substitution?

Answer 7

to solve simultaneous equations there are several methods that can be used;
graphing, substitution, elimination and matrices. the bottom line is the solution satisfies each equation.

for this problem lets use substitution.
we will divide the 2nd eqn by 3 since it can be factored and find the equivalent of x then we will substitute for x in the 1st eqn. this gives an equation with just one variable y. we solve for y then put this value back in the expression to find x.
It is a good practice to check the solution.

Answer 8

3x + 12y = 9
divide by 3 gives x + 4y = 3 means x = 3 - 4y
substituting in the 1st eqn 2x + 3y = 7
2(3 - 4y) + 3y = 7
6 - 8y + 3y = 7
y = -1/5
x = 3 - 4(-1/5) = (15 + 4)/5 = 19/5

check the ans in eqn 2
3x + 12 y = 9
left hand side
3*(19/5) + 12(-1/5) = (57-12)/5 = 45/5 = 9 = right hand side
and therefore correct solution 19/5, -1/5

Answer 9

to do the same problem by elimination you would multiply the 1st eqn by 4
and subtract the 2nd eqn. this will eliminate the y. solve the one variable eqn for x and then substitute to find y
2x + 3y = 7 multiply by 4 8x + 12 y = 28
subtract 2nd eqn 3x + 12y = 9
5x = 19 gives x = 19/5
you have x find y
3(19/5) + 12 y = 9
57/5 -9 = -12 y
divide by -12 so y = -1/5
different method same result

Answer 10

to graph: plot some points for each line and find where they intersect
to use matrices; will not cover that right now you have enough for now

Answer 11

do you have any questions?

Answer 12

Wow