Question

11. What is the value of xin the solution to this system of equations?

Answer 1

Answer:

x = ¹³⁄₂

y = ⁻¹⁄₂

Explanation:

$\bold{\begin{bmatrix}3x-5y=22\\ y=-5x+32\end{bmatrix}}$

• Substitute y = -5x + 32

$\bold{\begin{bmatrix}3x-5\left(-5x+32\right)=22\end{bmatrix}}$

• Simplify

$\bold{\begin{bmatrix}28x-160=22\end{bmatrix}}$

• Isolate x for 28x - 160 - 22: x = ¹³⁄₂

$\bold{\mathrm{For\:}y=-5x+32}$

• Substitute x = ¹³⁄₂

$\bold{y=-5\cdot \frac{13}{2}+32}$

-5 · ¹³⁄₂ + 32 = ⁻¹⁄₂

• y = ⁻¹⁄₂

x = ¹³⁄₂

y = ⁻¹⁄₂

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