Question

question 1 (2 points)
(06.03)
what are the solutions to the following system of equations?
y = x² + 3x - 7
3x - y = -2
a (3, 11) and (-3, -7)
b (11, 3) and (-3, -7)
c (3, 11) and (-7, -3)
d no real solutions

Explanation:

Step1: Solve the linear equation for y

From \( 3x - y = -2 \), we can rewrite it as \( y = 3x + 2 \).

Step2: Substitute y into the quadratic equation

Substitute \( y = 3x + 2 \) into \( y = x^2 + 3x - 7 \). So we have \( 3x + 2 = x^2 + 3x - 7 \).

Step3: Simplify the equation

Subtract \( 3x \) from both sides: \( 2 = x^2 - 7 \). Then add 7 to both sides: \( x^2 = 9 \).

Step4: Solve for x

Taking the square root of both sides, we get \( x = 3 \) or \( x = -3 \).

Step5: Find the corresponding y values

For \( x = 3 \), substitute into \( y = 3x + 2 \), \( y = 3(3)+2 = 11 \). For \( x = -3 \), substitute into \( y = 3x + 2 \), \( y = 3(-3)+2 = -7 \).

Answer:

a. \( (3, 11) \) and \( (-3, -7) \)