Question

solve using substitution.
-5x + 4y = 15
7x + y = 12
(\boxed{\quad}, \boxed{\quad})

Explanation:

Step1: Solve for y from the second equation

From \(7x + y = 12\), we can express \(y\) as \(y = 12 - 7x\).

Step2: Substitute y into the first equation

Substitute \(y = 12 - 7x\) into \(-5x + 4y = 15\). So we get \(-5x + 4(12 - 7x)=15\).

Step3: Simplify and solve for x

First, expand the equation: \(-5x + 48 - 28x = 15\). Combine like terms: \(-33x+48 = 15\). Subtract 48 from both sides: \(-33x=15 - 48=-33\). Then divide both sides by - 33: \(x = 1\).

Step4: Substitute x back to find y

Substitute \(x = 1\) into \(y = 12 - 7x\). Then \(y=12-7\times1 = 5\).

Answer:

\((1, 5)\)