To solve the system of equations given by 2x + 5y = 13 and 3x + 4y = 8, we can use the method of substitution or elimination. Here, we will use the elimination method.
First, let’s align our equations:
1) 2x + 5y = 13
2) 3x + 4y = 8
We want to eliminate one variable. To do this, we’ll first multiply the first equation by 3 and the second equation by 2 so that the coefficients of x match:
6x + 15y = 39 (Equation 1 multiplied by 3)
6x + 8y = 16 (Equation 2 multiplied by 2)
Now, we can subtract the second equation from the first:
(6x + 15y) – (6x + 8y) = 39 – 16
Which simplifies to:
7y = 23
Now, we can solve for y:
y = 23/7
Next, we substitute this value of y back into one of the original equations to solve for x. We’ll use the first equation:
2x + 5(23/7) = 13
2x + 115/7 = 13
2x = 13 – 115/7
2x = 91/7 – 115/7
2x = -24/7
x = -12/7
Thus, the solution to the system of equations is:
x = -12/7 and y = 23/7.
This means the values for x and y that satisfy both equations are -12/7 and 23/7, respectively.