# solve system using elimination: 4x - 3y = 11, 3x - 5y = -11

#### sum_one

##### New member
I have tried so hard to figure this one out, i just dont understand it :? .... plz help...

4x-3y =11 and 3x-5y = -11

#### jwpaine

##### Full Member
Re: solving systems using elimination=(

sum_one said:
I have tried so hard to figure this one out, i just dont understand it :? .... plz help...
4x-3y =11 and 3x-5y = -11
I see no work - it would be helpful to see what you have tried, so that we can correct you You have a system of two linear equations

4x-3y =11
3x-5y = -11

You are allowed to multiply each equation by any constant (as long as you do it to both sides of the equal sign) so that you can add / subtract terms.
What could you multiply the top equation by so that one of the terms is equal to another term in the other equation?

If you want the 3y term in the top equation to = 5y, than what would you have to multiply by? Divide 5y by 3y and you get (5/3). Therefore, (5/3)(3y) = 5y
If you can get one term from one equation which appears in the other equation, than you can add or subtract them to cancel them out... or "eliminate" that term.

You can, of course, multiply by a number so that you don't have any fractional terms.

Understood?

#### Loren

##### Senior Member
Re: solving systems using elimination=(

4x-3y =11
3x-5y = -11

Decide which variable you want to eliminate. If you decide on eliminating x, then multiply both sides of the first equation by 3 and both sides of the second equation by 4. Then subtract the second equation from the first equation (or visa versa). That will leave you with one equation with only the y variable. Solve for y. Then plug that result back into one of the original equations and solve for x.

If you decide to eliminate y in the original equations, then multiply both sides of the first equation by 5 and both sides of the second equation by 3. Then subtract one equation from the other and you will have one equation with one variable. etc.

#### Denis

##### Senior Member
4x-3y =11
3x-5y = -11

Another way: start by adding the equations: 7x - 8y = 0
7x = 8y
x = 8y / 7

Substitute that in either equations.