Question

fill in the blank 2.5 points use the substitution method to solve the linear system. enter your answer as a coordinate with parentheses and no spaces: (x,y) 2x + y = 2 x - 3y = 15 type your answer...

Explanation:

Step1: Solve for x from the second equation

From \( x - 3y = 15 \), we can express \( x \) as \( x = 3y + 15 \).

Step2: Substitute x into the first equation

Substitute \( x = 3y + 15 \) into \( 2x + y = 2 \). So we have \( 2(3y + 15) + y = 2 \).
Expand the left - hand side: \( 6y+30 + y=2 \).
Combine like terms: \( 7y+30 = 2 \).
Subtract 30 from both sides: \( 7y=2 - 30=-28 \).
Divide both sides by 7: \( y=\frac{-28}{7}=-4 \).

Step3: Substitute y back to find x

Substitute \( y = - 4 \) into \( x = 3y+15 \). Then \( x=3\times(-4)+15=-12 + 15 = 3 \).

Answer:

(3,-4)