solve 2x+3y=13 with 4x+5y=23
you are supposed to plug in the y to find the x
To solve the system of equations, we can use the method of substitution or the method of elimination. I will explain how to solve it using the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x:
2x + 3y = 13
Rearrange the equation to solve for x:
2x = 13 - 3y
x = (13 - 3y)/2
Step 2: Substitute the expression for x in terms of y into the other equation. Let's substitute x in the second equation:
4x + 5y = 23
4((13 - 3y)/2) + 5y = 23
Step 3: Simplify the equation and solve for y.
2(13 - 3y) + 5y = 23
26 - 6y + 5y = 23
26 - y = 23
-y = 23 - 26
-y = -3
y = 3
Step 4: Substitute the value of y back into one of the original equations to solve for x. Let's substitute y into the first equation:
2x + 3(3) = 13
2x + 9 = 13
2x = 13 - 9
2x = 4
x = 4/2
x = 2
So, the solution to the system of equations is x = 2 and y = 3.
2x + 3y = 13
4x + 5y = 23
multiply the first equation by 4, the second by 2, add:
8x + 12y = 52
subtract these two equations
8x + 10y = 46
______________
2y = 6 Divide 2
y=3