Solve the system of linear equations shown below. \( 2 a-3 b=18 \) \( 5 a+2 b=7 \) Fill in the blanks to write the solution in the form (a,b)

To solve the system of equations, we can use the substitution or elimination method. Let's use the elimination method here. First, we can multiply the first equation by 2 to align the coefficients of \( b \): 1. \( 4a - 6b = 36 \) (after multiplying the first equation by 2) 2. \( 5a + 2b = 7 \) Now, we can multiply the second equation by 3 to eliminate \( b \) later: 1. \( 4a - 6b = 36 \) 2. \( 15a + 6b = 21 \) (after multiplying the second equation by 3) Next, we add the two equations: \[ (4a - 6b) + (15a + 6b) = 36 + 21 \] This simplifies to: \[ 19a = 57 \] Now, solve for \( a \): \[ a = \frac{57}{19} = 3 \] Now, substitute \( a = 3 \) back into one of the original equations to find \( b \). Let's use the first equation: \[ 2(3) - 3b = 18 \] This simplifies to: \[ 6 - 3b = 18 \] Now, solve for \( b \): \[ -3b = 18 - 6 \Rightarrow -3b = 12 \Rightarrow b = -4 \] Thus, the solution in the form \( (a,b) \) is \( (3, -4) \).