To solve for [tex]\( y \)[/tex] in the equation
[tex]\[
-\frac{7}{4} y = -35,
\][/tex]
we need to isolate [tex]\( y \)[/tex]. We can do this by getting rid of the fraction that is multiplying [tex]\( y \)[/tex]. Here's how to proceed step by step:
1. Identify the coefficient of [tex]\( y \)[/tex]: In the equation, the coefficient of [tex]\( y \)[/tex] is [tex]\( -\frac{7}{4} \)[/tex].
2. Reciprocal of the coefficient: To isolate [tex]\( y \)[/tex], we can multiply both sides of the equation by the reciprocal of [tex]\( -\frac{7}{4} \)[/tex]. The reciprocal of [tex]\( -\frac{7}{4} \)[/tex] is [tex]\( -\frac{4}{7} \)[/tex].
3. Multiply both sides by the reciprocal: Now, multiply both sides of the equation by [tex]\( -\frac{4}{7} \)[/tex]:
[tex]\[
\left( -\frac{4}{7} \right) \left( -\frac{7}{4} y \right) = \left( -\frac{4}{7} \right)(-35).
\][/tex]
4. Simplify the left side: When you multiply [tex]\( -\frac{4}{7} \)[/tex] by [tex]\( -\frac{7}{4} \)[/tex], the [tex]\( y \)[/tex] on the left side remains because:
[tex]\[
\left( -\frac{4}{7} \right) \left( -\frac{7}{4} \right) = 1.
\][/tex]
Hence,
[tex]\[
1 \cdot y = y.
\][/tex]
5. Simplify the right side: Now, simplify the right side of the equation:
[tex]\[
-35 \cdot \left( -\frac{4}{7} \right) = 20.
\][/tex]
Therefore, the equation simplifies to:
[tex]\[
y = 20.
\][/tex]
So, the solution is:
[tex]\[
\boxed{20}.
\][/tex]
