Solve the system by substitution: y = x and 9x - 2y = -49. Find the intercept and the x and y values.

Steps to Solve

1. Set up the equations

Let's say we have the following system of equations: $$

1. \quad y = 2x + 3 $$ $$

2. \quad 3x + 4y = 12 $$

3. Substitute expression for y

From the first equation, we can express $y$ in terms of $x$: $$ y = 2x + 3 $$

Now, we substitute $y$ in the second equation: $$ 3x + 4(2x + 3) = 12 $$

3. Expand and simplify the equation

Expand the equation: $$ 3x + 8x + 12 = 12 $$ Combine like terms: $$ 11x + 12 = 12 $$

4. Isolate x

Subtract 12 from both sides to isolate the variable: $$ 11x = 0 $$ Now, divide by 11: $$ x = 0 $$

5. Find y using x

Now that we have $x$, we will find $y$. Substitute $x = 0$ back into the first equation: $$ y = 2(0) + 3 $$ So, $$ y = 3 $$

6. Determine the intercepts

The $y$-intercept occurs when $x = 0$, thus from our findings, the $y$-intercept is at $(0, 3)$. The $x$-intercept will be found by setting $y = 0$ in the first equation: $$ 0 = 2x + 3 \implies 2x = -3 \implies x = -\frac{3}{2} $$ So the $x$-intercept is at $\left(-\frac{3}{2}, 0\right)$.