I've been stuck for a while on this problem
Which ordered pair represents the solution to the system of equations?
{ 5x+3y=7
{ 3x-5y=-23
5x+3y=7 ...........(1)
3x-5y=-23 .........(2)
We try to cancel/eliminate one of the variables. I choose to eliminate y.
25x+15y=35 ...........5*(1)....(1A)
9x-15y=-69 .........3*(2).....(2A)
Add (1A)+(2A)
34x=-34
Solve for x.
Substitute value of x into 1 and solve for y.
To find the solution to this system of equations, you can use the method of solving systems of linear equations called "substitution." Here's how you can do it:
Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve the first equation for x in terms of y:
5x + 3y = 7
5x = 7 - 3y
x = (7 - 3y)/5.
Step 2: Substitute the expression for that variable into the other equation. Let's substitute the expression for x in terms of y into the second equation:
3x - 5y = -23
3((7 - 3y)/5) - 5y = -23.
Step 3: Simplify and solve for y:
(21 - 9y)/5 - 5y = -23
(21 - 9y) - 25y = -115.
Step 4: Simplify and solve for y:
21 - 9y - 25y = -115
-34y = -136
y = -136/-34
y = 4.
Step 5: Substitute the found value of y into either of the original equations to solve for x. Let's use the first equation:
5x + 3(4) = 7
5x + 12 = 7
5x = 7 - 12
5x = -5
x = -5/5
x = -1.
Therefore, the ordered pair (x, y) that represents the solution to the system of equations is (-1, 4).