Question

1. a system of linear equations is given.

$3x + 2y = 7$
$2x - 3y = -4$
what are the x- and y-values of the solution to the system?
write your answer in the boxes using the digits 0 through 9, the decimal, or the negative sign. you may use up to seven characters.
$x = \boxed{}$
$y = \boxed{}$

Explanation:

Step1: Eliminate one variable (e.g., y)

Multiply the first equation by 3: \(3(3x + 2y) = 3\times7\) gives \(9x + 6y = 21\).
Multiply the second equation by 2: \(2(2x - 3y) = 2\times(-4)\) gives \(4x - 6y = -8\).

Step2: Add the two new equations

Add \(9x + 6y = 21\) and \(4x - 6y = -8\):
\((9x + 4x) + (6y - 6y) = 21 + (-8)\)
\(13x = 13\)

Step3: Solve for x

Divide both sides by 13: \(x = \frac{13}{13} = 1\).

Step4: Substitute x = 1 into first equation

Substitute \(x = 1\) into \(3x + 2y = 7\):
\(3(1) + 2y = 7\)
\(3 + 2y = 7\)

Step5: Solve for y

Subtract 3 from both sides: \(2y = 7 - 3 = 4\).
Divide by 2: \(y = \frac{4}{2} = 2\).

Answer:

\(x = 1\)
\(y = 2\)